Homotopy lifting property for actions of finite abelian groups on Hausdorff topological spaces
Eduardo Blanco-Gómez
本文证明了有限阿贝尔群在豪斯多夫拓扑空间上的作用满足同伦提升性质。
本文证明了有限阿贝尔群在豪斯多夫拓扑空间上的作用具有同伦提升性质。
In this paper we prove the homotopy lifting property for actions of finite abelian groups on Hausdorff topological spaces.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Homotopy lifting property in symmetric products
本文证明了Hausdorff空间X的对称积SP_m(X)和F_m(X)满足同伦提升性质，并引入拓扑拼图理论来分解X^m。
In classical homotopy theory, two spaces are homotopy equivalent if one space can be continuously deformed into the other. This theory, however, does not respect the discrete nature of graphs. For this reason, a discrete homotopy theory that recognizes the difference between the vertices and edges of a graph was invented, called A-homotopy theory [1-5]. In classical homotopy theory, covering spaces and lifting properties are often used to compute the fundamental group of the circle. In this paper, we develop the lifting properties for A-homotopy theory. Using a covering graph and these lifting…
The paper is devoted to introduce some notions extending the unique path lifting property from a homotopy viewpoint and to study their roles in the category of fibrations. First, we define some homotopical kinds of the unique path lifting property and find all possible relationships between them. Moreover, we supplement the full relationships of these new notions in the presence of fibrations. Second, we deduce some results in the category of fibrations with these notions instead of unique path lifting such as the existence of products and coproducts. Also, we give a brief comparison of these …
We use Quillen model structures to show a systematic method to lift recollements of hereditary abelian model categories to recollements of their associated homotopy categories. To that end, we use the notion of Quillen adjoint triples and we investigate transfers of abelian model structures along adjoint pairs. Applications include liftings of recollements of module categories to their derived counterpart, liftings to homotopy categories that provide models for stable categories of Gorenstein projective and injective modules and liftings to homotopy categories of n-morphism categories over Iwa…
This paper is the second in a series exploring the properties of a functor which assigns a homotopy double groupoid with connections to a Hausdorff space. We show that this functor satisfies a version of the van Kampen theorem, and so is a suitable tool for nonabelian, 2-dimensional, local-to-global problems. The methods are analogous to those developed by Brown and Higgins for similar theorems for other higher homotopy groupoids. An integral part of the proof is a detailed discussion of commutative cubes in a double category with connections, and a proof of the key result that any composition…
For any finite group $G$, we define the notion of a Bredon homotopy action of $G$, modelled on the diagram of fixed point sets $(X_H)_{H\leq G}$ for a $G$-space $X$, together with a pointed homotopy action of the group $N_{G}H/H$ on $X^{H}/(\bigcup_{H<K} X^{K})$. We then describe a procedure for constructing a suitable diagram $\underline{X}:O_G^{op}\to Top$ from this data, by solving a sequence of elementary lifting problems. If successful, we obtain a $G$-space $X'$ realizing the given homotopy information, determined up to Bredon $G$-homotopy type. Such lifting methods may also be used to u…
The settings for homotopical algebra---categories such as simplicial groups, simplicial rings, $A_\infty$ spaces, $E_\infty$ ring spectra, etc.---are often equivalent to categories of algebras over some monad or triple $T$. In such cases, $T$ is acting on a nice simplicial model category in such a way that $T$ descends to a monad on the homotopy category and defines a category of homotopy $T$-algebras. In this setting there is a forgetful functor from the homotopy category of $T$-algebras to the category of homotopy $T$-algebras. Under suitable hypotheses we provide an obstruction theory, in t…
Given a suitable functor T:C -> D between model categories, we define a long exact sequence relating the homotopy groups of any X in C with those of TX, and use this to describe an obstruction theory for lifting an object G in D to C. Examples include finding spaces with given homology or homotopy groups.
The homotopy types of directed path and trace spaces
构造饱和有向空间，使两点间迹空间同胚于正方形而有向路径空间有非平凡基本群，证明典范商映射非弱同伦等价，结论对正则路径亦成立。
On maps with continuous path lifting
本文研究具有连续路径覆盖性质的映射，证明其严格介于Hurewicz与Serre纤维化之间，并利用拓扑基本群给出了此类映射的完整分类。
Let Y be an absolute neighborhood retract (ANR) for the class of metric spaces and let X be a Hausdorff space. Let map(X,Y) denote the space of continuous maps from X to Y with the compact open topology. It is shown that if X is a CW complex then map(X,Y) is an ANR for the class of metric spaces if and only if map(X,Y) is metrizable and has the homotopy type of a CW complex. The same holds also when X is a compactly generated hemicompact space (metrizability assumption is void in this case).
$G\operatorname{-CGWH}$ spaces and their (homotopy) colimits
本文研究带紧李群$G$作用的紧生成弱豪斯多夫空间及其余极限、同伦余极限，探讨（同伦）余极限与映射空间及同伦群的关系。
In this paper, using the topology on the set of shape morphisms between arbitrary topological spaces $X$, $Y$, $Sh(X,Y)$, defined by Cuchillo-Ibanez et al. in 1999, we consider a topology on the shape homotopy groups of arbitrary topological spaces which make them Hausdorff topological groups. We then exhibit an example in which $\checkπ_k^{top}$ succeeds in distinguishing the shape type of $X$ and $Y$ while $\checkπ_k$ fails, for all $k\in \Bbb{N}$. Moreover, we present some basic properties of topological shape homotopy groups, among them commutativity of $\checkπ_k^{top}$ with finite produc…
In this paper, we aim to establish a new shape theory, compact Hausdorff shape (CH-shape) for general Hausdorff spaces. We use the "internal" method and direct system approach on the homotopy category of compact Hausdorff spaces. Such a construction can preserve most good properties of H-shape given by Rubin and Sanders. Most importantly, we can moreover develop the entire homology theory for CH-shape, including the exactness, dual to the consequence of Mardešić and Segal.
Uchillo-Ibanez et al. introduced a topology on the sets of shape morphisms between arbitrary topological spaces in 1999. In this paper, applying a similar idea, we introduce a topology on the set of coarse shape morphisms $Sh^*(X,Y)$, for arbitrary topological spaces $X$ and $Y$. In particular, we can consider a topology on the coarse shape homotopy group of a topological space $(X,x)$, $Sh^*((S^k,*),(X,x))=\checkπ_k^{*}(X,x)$, which makes it a Hausdorff topological group. Moreover, we study some properties of these topological coarse shape homotopoy groups such as second countability, movabil…
In this paper we define the notion of pullback lifting of a lifting crossed module over a crossed module morphism and interpret this notion in the category of group-groupoid actions as pullback action. Moreover, we give a criterion for the lifting of homotopic crossed module morphisms to be homotopic, which will be called homotopy lifting property for crossed module morphisms. Finally, we investigate some properties of derivations of lifting crossed modules according to base crossed module derivations.
Let $X$ and $Y$ be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group $G$. Assuming that $Y$ is $d$-connected and $\dim X\le 2d$, for some $d\geq 1$, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps $|X|\to|Y|$; the existence of such a map can be decided even for $\dim X\leq 2d+1$. For fixed $G$ and $d$, the algorithm runs in polynomial time. This yields the first algorithm for deciding topological embeddability of a $k$-dimensional finite simplicial complex int…
Homotopy groups of symmetric products
本文证明了豪斯多夫拓扑空间$X$的对称积$SP_{m}(X)$与$F_{m}(X)$的同伦群为单态，并引入不连续同伦群这一新代数工具。
A necessary condition for liftings of positive characteristic varieties with finite fundamental groups
研究具有有限基本群的正特征簇提升到特征零的必要条件，基于平展同伦理论和沃尔有限性障碍，通过定义模l有限支配性概念，证明簇提升的链复形条件，还扩展了沃尔有限性障碍讨论。
We construct a space $\mathbb{P}$ for which the canonical homomorphism $π_1(\mathbb{P},p) \rightarrow \checkπ_1(\mathbb{P},p)$ from the fundamental group to the first Čech homotopy group is not injective, although it has all of the following properties: (1) $\mathbb{P}\setminus\{p\}$ is a 2-manifold with connected non-compact boundary; (2) $\mathbb{P}$ is connected and locally path connected; (3) $\mathbb{P}$ is strongly homotopically Hausdorff; (4) $\mathbb{P}$ is homotopically path Hausdorff; (5) $\mathbb{P}$ is 1-UV$_0$; (6) $\mathbb{P}$ admits a simply connected generalized covering space …
The quasitopological fundamental group $π_{1}^{qtop}(X,x_0)$ is the fundamental group endowed with the natural quotient topology inherited from the space of based loops and is typically non-discrete when $X$ does not admit a traditional universal cover. This topologized fundamental group is an invariant of homotopy type which has the ability to distinguish weakly homotopy equivalent and shape equivalent spaces. In this paper, we clarify various relationships among topological properties of the group $π_{1}^{qtop}(X,x_0)$ and properties of the underlying space $X$ such as `$π_{1}$-shape injecti…
Let $M$ be a topological monoid with homotopy group completion $ΩBM$. Under a strong homotopy commutativity hypothesis on $M$, we show that $π_k (ΩBM)$ is the quotient of the monoid of free homotopy classes $[S^k, M]$ by its submonoid of nullhomotopic maps. We give two applications. First, this result gives a concrete description of the Lawson homology of a complex projective variety in terms of point-wise addition of spherical families of effective algebraic cycles. Second, we apply this result to monoids built from the unitary, or general linear, representation spaces of discrete groups, lea…
We study notions of persistent homotopy groups of compact metric spaces together with their stability properties in the Gromov-Hausdorff sense. We pay particular attention to the case of fundamental groups, for which we obtain a more precise description. Under fairly mild assumptions on the spaces, we proved that the classical fundamental group has an underlying tree-like structure (i.e. a dendrogram) and an associated ultra-metric.
In this paper we recover Bousfield's computation of $ν_1$-periodic homotopy groups of simply connected, finite $H$-spaces from \cite{Bou99} using the techniques of Goodwillie calculus. This is done through first computing André-Quillen cohomology over the monad $\mathbb{T}$ that encodes the power operations of complex $K$-theory. Then lifting this computation to computing $K$-theory of topological André-Quillen cohomology, and then using results of Behrens and Rezk relating it back to the Bousfield-Kuhn functor. The fact that we recovers the result of Bousfield allows us to conclude $ν_1$-peri…
Lifting $N_\infty$ operads from conjugacy data
该研究提出无损群的概念，证明这类群上的$G$-$N_\infty$操作子同伦类与共轭类偏序集上的限制传递系统一一对应，为操作子同伦分类提供了新的群论视角。
In a previous paper [21] the author studied the homotopy lifting property in the category dTop of directed spaces in the sense of M. Grandis [12], [13], [14]. The present paper, which is a continuation of aforementioned article, introduces and studies the directed weak homotopy property (dWCHP) and directed weak fibrations, extending to the category dTop the well known Dold's (or weak) - fibrations [6]. The dWCHP is characterized in several ways. Then the notion of a directed fibre homotopy equivalence (dFHE) between directed weak fibrations is studied. Some examples and counterexamples are gi…
Topological Complexity Related To Multi-Valued Functions
本文研究多值函数理论中的机器人运动规划问题，通过引入多同伦提升性质和多纤维化丰富多同伦研究，并计算了空间或多纤维化的拓扑多复杂度与Lusternik-Schnirelmann多维数。
Homotopy, homology, and persistent homology using closure spaces
本文在 Čech 闭包空间滤过上构建多种同伦与奇异同调理论以生成持续模，并推广 Gromov-Hausdorff 距离证明其稳定性。
If P \to X is a topological principal K-bundle and \hat K a central extension of K by Z, then there is a natural obstruction class δ_1(P) in \check H^2(X,\uline Z) in sheaf cohomology whose vanishing is equivalent to the existence of a \hat K-bundle \hat P over X with P \cong \hat P/Z. In this paper we establish a link between homotopy theoretic data and the obstruction class δ_1(P) which in many cases can be used to calculate this class in explicit terms. Writing \partial_d^P \: π_d(X) \to π_{d-1}(K) for the connecting maps in the long exact homotopy sequence, two of our main results can be f…
The Brouwer fixed point theorem states that the disk $D^n$ has the fixed point property. More generally, by the Lefschetz fixed point theorem any compact ANR with trivial rational homology has the fixed point property. In this note we prove that for any connected compact CW-complex $K$ there exists a space $X$ weak homotopy equivalent to $K$ which has the fixed point property. The result is known to be false if we require $X$ to be a polyhedron. The space $X$ we construct is a non-Hausdorff space with finitely many points.
Function-Rips complexes in persistent homotopy theory: Stability and persistent Latschev theorems
本文研究了函数-里普斯复形在持久同伦论中的稳定性及持久拉茨谢夫定理，通过结合固定尺度的里普斯复形与底层空间的滤波数据，推广了拉茨谢夫和哈斯曼的经典结果到具有滤波函数的空间中。
We introduce the notion of smooth cell complexes and its subclass consisting of gathered cell complexes within the category of diffeological spaces (cf. Definitions 1 and 3). It is shown that the following hold. (1) With respect to the D-topology, every smooth cell complex is a topological cell complex (cf. Proposition 2). It is paracompact and Hausdorff if it is countable (cf. Proposition 8). (2) Every continuous map between gathered cell complexes is continuously homotopic to a smooth map (cf. Theorem 5). (3) Any topological cell complex is continuously homotopy equivalent to a gathered (hen…
We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G-homotopy theory is "pieced together" from the G/U-homotopy theories for suitable quotient groups G/U of G; a motivation is the way continuous group cohomology of a profinite group is built out of the cohomology of its finite quotient groups. In the model category of equivariant spectra Postnikov towers are studied from a general perspective. We introduce pro-G-spectra and construct various model structures on them. A key pr…
Second homotopy classes associated with non-cancellative monoids
本文通过CW复形基本群的半正基本关系定义非消去幺半群，构造其非消去元组孪生体对应的第二同伦类，并成功重构了Akio Hattori研究的generic lines arrangement补集的第二同伦类，为后续椭圆判别式轨迹补集的应用奠定基础。
Let $G$ be a compact connected Lie group and let $ξ,ν$ be complex vector bundles over the classifying space $BG$. The problem we consider is whether $ξ$ contains a subbundle which is isomorphic to $ν$. The necessary condition is that for every prime $p$ the restriction $ξ|_{BN_p^G}$, where $N_p^G$ is a maximal $p$-toral subgroup of $G$, contains a subbundle isomorphic to $ν|_{BN_p^G}$. We provide a criterion when this condition is sufficient, expressed in terms of $Λ^*$-functors of Jackowski, McClure \& Oliver and we prove that this criterion applies if $ν$ is a universal bundle over $BU(n)$. …
We consider the topological and geometric reconstruction of a geodesic subspace of $\mathbb{R}^N$ both from the Čech and Vietoris-Rips filtrations on a finite, Hausdorff-close, Euclidean sample. Our reconstruction technique leverages the intrinsic length metric induced by the geodesics on the subspace. We consider the distortion and convexity radius as our sampling parameters for a successful reconstruction. For a geodesic subspace with finite distortion and positive convexity radius, we guarantee a correct computation of its homotopy and homology groups from the sample. For geodesic subspaces…
Shape theory works nice for (Hausdorff) paracompact spaces, but for spaces with no separation axioms, it seems to be quite poor. However, for finite and locally finite spaces their weak homotopy type is rather rich, and is equivalent to the weak homotopy type of finite and locally finite polynedra, respectively. In the paper there is proposed a variant of shape theory called quasi-shape, which suits both paracompact and locally finite spaces, i.e. the quas-shape is isomorphic to the weak homotopy type for locally finite spaces, and is \natural-equivalent to the ordinary shape in the case of pa…
Persistent Sullivan Minimal Models of Metric Spaces
本文提出持久 Sullivan 极小模型将经典有理同伦论扩展至拓扑数据分析，证明了其在 CDGAs 同伦范畴中的交错距离稳定性，并提供了比持久同调更具辨别力的不变量及更尖锐的 Gromov-Hausdorff 距离下界。
For any $n\geq k\geq l\in\mathbb{N},$ let $S(n,k,l)$ be the set of all those non-negative definite matrices $a\in M_{n}(\mathbb{C})$ with $l\leq\text{rank }a\leq k$. Motivated by applications to $C^{*}$-algebra theory, we investigate the homotopy properties of continuous maps from a compact Hausdorff space $X$ into sets of the form $S(n,k,l).$ It is known that for any $n,$ if $k-l$ is approximately 4 times the covering dimension of $X$ then there is only one homotopy class of maps from $X$ into $S(n,k,l)$, i.e. $C(X,S(n,k,l))$ is path connected. In our main Theorem we improve this bound by a f…
We show that the categories PsTop and Lim of pseudotopological spaces and limit spaces, respectively, admit cofibration category structures, and that PsTop admits a model category structure, giving several ways to simultaneously study the homotopy theory of classical topological spaces, combinatorial spaces such as graphs and matroids, and metric spaces endowed with a privileged scale, in addition to spaces of maps between them. In the process, we give a sufficient condition for a topological construct which contains compactly generated Hausdorff spaces as a subcategory to admit an $I$-categor…
The topological fundamental group $π_{1}^{top}$ is a homotopy invariant finer than the usual fundamental group. It assigns to each space a quasitopological group and is discrete on spaces which admit universal covers. For an arbitrary space $X$, we compute the topological fundamental group of the suspension space $Σ(X_+)$ and find that $π_{1}^{top}(Σ(X_+))$ either fails to be a topological group or is the free topological group on the path component space of $X$. Using this computation, we provide an abundance of counterexamples to the assertion that all topological fundamental groups are topo…
We show that there are homotopy equivalences $h:N\to M$ between closed manifolds which are induced by cell-like maps $p:N\to X$ and $q:M\to X$ but which are not homotopic to homeomorphisms. The phenomenon is based on construction of cell-like maps that kill certain $\mathbb L$-classes. The image space in these constructions is necessarily infinite-dimensional. In dimension $>6$ we classify all such homotopy equivalences. As an application, we show that such homotopy equivalences are realized by deformations of Riemannian manifolds in Gromov-Hausdorff space preserving a contractibility function…
Continuous Comparison of Free Simplicial Prounipotent and Pro-$p$ Resolutions
本文给出原幂零与pro-$p$群范畴中自由单纯形分解比较定理的连续版本，通过连续线性分裂或投射性实现提升，并确立同伦唯一性。
We study liftings of abelian model structures to categories of chain complexes and construct a realization functor from the derived category of a Grothendieck abelian category equipped with a cofibrantly generated, hereditary abelian model structure to the homotopy category of that model structure.
The theory of dendroidal sets has been developed to serve as a combinatorial model for homotopy coherent operads by Moerdijk and Weiss. An infinity-operad is a dendroidal set D satisfying certain lifting conditions. In this paper we give a definition of K-groups K_n(D) for a dendroidal set D. These groups generalize the K-theory of symmetric monoidal (resp. permutative) categories and algebraic K-theory of rings. We establish some useful properties like invariance under the appropriate equivalences and long exact sequences which allow us to compute these groups in some examples. We show that t…
We undertake a systematic study of the notion of fibration in the setting of abstract simplicial complexes, where the concept of `homotopy' has been replaced by that of `contiguity'. Then a fibration will be a simplicial map satisfying the `contiguity lifting property'. This definition turns out to be equivalent to a known notion introduced by G. Minian, established in terms of a cylinder construction $K \times I_m$. This allows us to prove several properties of simplicial fibrations which are analogous to the classical ones in the topological setting, for instance: all the fibers of a fibrati…
A stratified space is a topological space together with a decomposition into strata corresponding to different types of singularities. Examples of such spaces appear everywhere in topology and geometry. The study of stratified spaces involves invariants such as intersection cohomology which are only invariants under stratification-preserving homotopies. In this thesis, we study the homotopy theory of stratified spaces with respect to those stratified homotopies. To do so, we construct model categories for stratified spaces and we introduce new invariants to characterize them, the filtered homo…
We define Peano covering maps and prove basic properties analogous to classical covers. Their domain is always locally path-connected but the range may be an arbitrary topological space. One of characterizations of Peano covering maps is via the uniqueness of homotopy lifting property for all locally path-connected spaces. Regular Peano covering maps over path-connected spaces are shown to be identical with generalized regular covering maps introduced by Fischer and Zastrow. If $X$ is path-connected, then every Peano covering map is equivalent to the projection $\widetilde X/H\to X$, where $H$…
We present a novel approach to the problem of integrating homotopy Lie algebras by representing the Maurer-Cartan space functor with a universal cosimplicial object. This recovers Getzler's original functor but allows us to prove the existence of additional, previously unknown, structures and properties. Namely, we introduce a well-behaved left adjoint functor, we establish functoriality with respect to infinity-morphisms, and we construct a coherent hierarchy of higher Baker-Campbell-Hausdorff formulas. Thanks to these tools, we are able to establish the most important results of higher Lie t…
We apply the Gromov-Hausdorff metric $d_G$ for characterization of certain generalized manifolds. Previously, we have proved that with respect to the metric $d_G,$ generalized $n$-manifolds are limits of spaces which are obtained by gluing two topological $n$-manifolds by a controlled homotopy equivalence (the so-called $2$-patch spaces). In the present paper, we consider the so-called {\sl manifold-like} generalized $n$-manifolds $X^{n},$ introduced in 1966 by Mardešić and Segal, which are characterized by the existence of $δ$-mappings $f_δ$ of $X^n$ onto closed manifolds $M^{n}_δ,$ for arbit…
In this paper, we examine how topological complexity, simplicial complexity, discrete topological complexity, and combinatorial complexity compare when applied to models of $S^1$. We prove that the topological complexity of non-minimal finite models of $S^1$ can be less-than-or-equal-to 3, and that the TC of the minimal finite model of any $n$-sphere is equal to 4 for $n \geq 1$. We show the former using properties of the LS-category, and we show the latter by proving that the TC of the non-Hausdorff suspension of any finite connected $T_0$ space is equal to 4. We also prove a result about the…
Elements of higher homotopy groups undetectable by polyhedral approximation
本文利用高阶Spanier群刻画了多面体逼近无法检测的高阶同伦群元素，证明了在特定拓扑条件下该核等于第n阶Spanier群，并推广了Kozlowski-Segal定理。
By generalizing the whisker topology on the $n$th homotopy group of pointed space $(X, x_0)$, denoted by $π_n^{wh}(X, x_0)$, we show that $π_n^{wh}(X, x_0)$ is a topological group if $n \ge 2$. Also, we present some necessary and sufficient conditions for $π_n^{wh}(X,x_0)$ to be discrete, Hausdorff and indiscrete. Then we prove that $L_n(X,x_0)$ the natural epimorphic image of the Hawaiian group $\mathcal{H}_n(X, x_0)$ is equal to the set of all classes of convergent sequences to the identity in $π_n^{wh}(X, x_0)$. As a consequence, we show that $L_n(X, x_0) \cong L_n(Y, y_0)$ if $π_n^{wh}(X, …
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics. We consider the extension of classical 2-dimensional topological quantum field theories to Klein topological quantum field theories which allow unorientable surfaces. We generalise open topological conformal field theories to open Klein topological conformal field theories and c…
Topological Stability and Latschev-type Reconstruction Theorems for Spaces of Curvature Bounded Above
本文提出了一种基于路径度量的重建方法，用于具有上界曲率的空间的同伦类型重建，并首次建立了在可达性和μ-可达性消失情况下的重建保证。
The 2-primary Hurewicz image of tmf
本文通过改进的 Adams 谱序列、tmf-分解及 M(8,v_1^8) 上的 v_2^32-自映射，确定了 2-主 tmf-Hurewicz 同态的像，并生成球面稳定同伦群中的 192-周期族。
Let $H$ be a subgroup of $π_{1}(X,x_{0})$. In this paper, we extend the concept of $X$ being SLT space to $H$-SLT space at $x_0$. First, we show that the fibers of the endpoint projection $p_{H}:\tilde{X}_{H}\rightarrow X$ are topological group when $X$ is $H$-SLT space at $x_0$ and $H$ is a normal subgroup. Also, we show that under these conditions the concepts of homotopically path Hausdorff relative to $H$ and homotopically Hausdorff relative to $H$ coincide. Moreover, among other things, we show that the endpoint projection map $p_{H}$ has the unique path lifting property if and only if $H…
A homotopy orbit spectrum for profinite groups
本文为 profinite 群定义了 $S[[G]]$-模及同伦轨道谱 $X_{hG}$，给出了其同伦轨道谱序列 $E_2$-项同构于群同调逆向极限的条件，并证明了在紧 Hausdorff 群连续作用等情形下该条件成立。
G-kernels and Crossed Modules
该研究基于拓扑交叉模构建统一框架处理Γ-核的提升障碍，建立其与上同调集的对应，分析相关分类空间性质，并在强自吸收代数情形下证明同伦集的群结构及自然变换的群同构性。
This paper proves that the two homotopy theories for orbispaces given by Gepner and Henriques and by Schwede, respectively, agree by providing a zig-zag of Dwyer-Kan equivalences between the respective topologically enriched index categories. The aforementioned authors establish various models for unstable global homotopy theory with compact Lie group isotropy, and orbispaces serve as a common denominator for their particular approaches. Although the two flavors of orbispaces are expected to agree with each other, a concrete comparison zig-zag has not been known so far. We bridge this gap by p…
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。