Sam Hagh Shenas Noshari
$Γ$-symmetric spaces are a vast generalization of symmetric spaces. Previous results make it conceivable that their isotropy action is equivariantly formal, and we provide evidence for this in case that $Γ= \mathbb{Z}_2\times\mathbb{Z}_k$. This in particular implies that $\mathbb{Z}_2\times\mathbb{Z}_k$-symmetric spaces are formal in the sense of Rational Homotopy Theory.
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
Equivariant smooth Deligne cohomology
在Brylinski工作的基础上，我们引入了等变光滑Deligne上同调群的概念，它是普通光滑Deligne上同调群和普通等变上同调群的推广.利用上同调群，我们对具有联络的等变圆丛和具有联络的等变格进行了分类。
For a compact Lie group acting on a smooth manifold, we define the differential cohomology of a certain quotient stack involving principal bundles with connection. This produces differential equivariant cohomology groups that map to the Cartan-Weil equivariant forms and to Borel's equivariant integral cohomology. We show the Chern-Weil homomorphism for equivariant vector bundles with connection naturally factors through differential equivariant cohomology.
Chern-Weil homomorphism in twisted equivariant cohomology
我们描述了扭曲等变上同调的Cartan和Weil模型以及两者之间的Cartan同态，并将Chern-Weil同态推广到扭曲等变上同调。阐明了为了建立上同调理论，扭曲等变上同调的系数必须取在$G$的对偶李代数上的完备多项式代数中.我们回顾了精确Courant代数胚的等变上同调和扭曲的等变上同调之间的关系，并展示了如何赋予Borel构造$M\times_G EG_k$的有限维近似的广义复结构，只要广义复流形$M$具有Hamilton $G$作用。
This is a survey on the equivariant cohomology of Lie group actions on manifolds, from the point of view of de Rham theory. Emphasis is put on the notion of equivariant formality, as well as on applications to ordinary cohomology and to fixed points.
We construct and analyse models of equivariant cohomology for differentiable stacks with Lie group actions extending classical results for smooth manifolds due to Borel, Cartan and Getzler. We also derive various spectral sequences for the equivariant cohomology of a differentiable stack generalising among others Bott's spectral sequence which converges to the cohomology of the classifying space of a Lie group.
Equivariant cohomology of quaternionic flag manifolds
本文的主要结果是$\mathbb{H}^n$中所有完备旗流形$Fl_n(\mathbb{H})$的$Sp(1)^n$ -等变上同调环的Borel型刻画。为了证明这一点，我们得到了该环的Goresky-Kottwitz-MacPherson型描述。
We compute the rational Borel equivariant cohomology ring of a cohomogeneity-one action of a compact Lie group.
We construct a deformed Morse complex computing the equivariant cohomology of a manifold M endowed with a smooth S^1-action. The deformation of the coboundary operator is given by counting gradient flow lines of a Morse function f that are allowed to "jump" along orbits of the S^1-action for finite time intervalls.
The construction of characteristic classes via the curvature form of a connection is one motivation for the refinement of integral cohomology by de Rham cocycles -- known as differential cohomology. We will discuss the analog in the case of a group action on the manifold: The definition of equivariant characteristic forms in the Cartan model due to Nicole Berline and Michèle Vergne motivates a refinement of equivariant integral cohomology by all Cartan cocycles. In view of this, we will also review previous definitions critically, in particular the one given by Kiyonori Gomi.
Extended manifolds and extended equivariant cohomology
我们定义了具有扩展的切丛的流形范畴，研究了它们的对称性，并考虑了这一范畴中李群作用的等变上同调的类似性。我们表明，当行动保持分裂的扩展切丛，我们的定义的扩展等变上同调同意扭曲等变德拉姆模型的Cartan，并在这种情况下，我们表明，有本地化的不动点集，à la Atiyah-Bott。
A refined form of the `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type was established by the authors in the context of manifolds with corners; the canonical construction induces fibrations on the boundary faces of the resolution resulting in an `equivariant resolution structure'. Here, equivariant K-theory and the Cartan model for equivariant cohomology are tracked under the resolution procedure as is the delocalized equivariant cohomology of Baum, Brylinski and MacPherson. This leads to resolved models…
The `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a `resolution tower' which projects to a resolution, with iterated boundary fibration, of the quotient. Equivariant K-theory and the Cartan model for equivariant cohomology are tracked under the resolution procedure as is the delocalized equivariant cohomology of Baum, Brylinski and MacPherson. This leads to resolv…
Equivariant cohomology and the Maurer-Cartan equation
设G是光滑作用在流形M上的紧致连通李群. Goresky-Kottwitz-MacPherson描述了M的等变上同调的小Cartan模型，拟同构于等变微分形式的标准Cartan复形。本文构造了一个从小Cartan模型到标准Cartan模型的显式上链映射，导出了一个上同调同构。该结构涉及一个显着的非齐次Maurer-Cartan方程的解决方案。这个解在Weil代数的海侵理论和主丛的上同调的Chevalley-Koszul理论中有进一步的应用。
In this note we prove an equivariant version of a result of Cartan for equivariant simplicial cohomology with local coefficients.
We introduce equivariant twisted cohomology of a simplicial set equipped with simplicial action of a discrete group and prove that for suitable twisting function induced from a given equivariant local coefficients, the simplicial version of Bredon-Illman cohomology with local coefficients is isomorphic to equivariant twisted cohomology. The main aim of this paper is to prove a classification theorem for equivariant simplicial cohomology with local coefficients.
In this paper, we compute the $RO(\mathbb{Z}/2)$-graded equivariant cohomology of rotation groups and Stiefel manifolds with particular involutions.
Equivariant K-theory and Equivariant Cohomology
对交换紧李群T，利用等变上同调给出了复系数T-等变K-理论的一个刻画。在附录中，我们通过将Chang-Skjelbred和Goresky-Kottwitz-MacPherson的结果从等变上同调推广到等变K-理论给出了这一应用。
We give Leray-Borel-type descriptions for the mod-$2$ and the rational equivariant cohomology rings of the real and the oriented flag manifolds under the canonical torus or 2-torus actions.
The Witten genus and equivariant elliptic cohomology
我们构造了复等变椭圆上同调的Thom类，推广了等变Witten亏格.这给出了一个新的证明刚性的威滕属，表现出密切的关系，最近的工作非等变方向的椭圆谱。
We calculate the integral equivariant cohomology, in terms of generators and relations, of locally standard torus orbifolds whose odd degree ordinary cohomology vanishes. We begin by studying GKM-orbifolds, which are more general, before specialising to half-dimensional torus actions.
In this paper, we calculate $RO(C_2)$-graded cohomology of $C_2$-equivariant Eilenberg-Mac Lane spaces $K(\underline{Z/2}, n+σ)$ for $n\geq 0$. These can be used to give the relation between equivariant lambda algebra and equivariant Adams resolution and equivariant unstable Adams spectral sequence, which are defined in author`s dissertation.
We prove the equivariant Leray-Hirsch theorem combinatorially for sufficiently good torus equivariant fiber bundles consisting of homogeneous spaces of Lie groups. We apply this theorem to determining the equivariant integral cohomology ring of the flag manifold of type $E_6$ and express it explicitly as a quotient ring of a polynomial ring.
We study the Duflot filtration on the Borel equivariant cohomology of smooth manifolds with a smooth $p$-torus action. We axiomatize the filtration and prove analog of several structural results about equivariant cohomology rings in this setting. We apply this abstract theory to study the $\mathbb{F}_p$ cohomology rings of classifying spaces of compact Lie groups, and show how to recover geometric results about the cohomology of $BG$ using equivariant cohomology. This includes some results about detection on subgroups and restrictions on associated primes that were previously only known for fi…
Equivariant Cohomology and Representations of the Symmetric Group
研究了空间中n点的位形空间与U（n）的旗流形之间的等变映射的上同调。
This paper determines the RO(G)-graded Eilenberg-MacLane cohomology of the real, infinite, equivariant Grassmannians in the case G=Z/2. Possible connections with motivic characteristic classes for quadratic bundles are briefly discussed.
We compute the $RO(C_2)$-graded Bredon cohomology of certain families of real and complex $C_2$-equivariant Grassmannians.
Equivariant cohomology distinguishes toric manifolds
具有群作用的空间的等变上同调不仅是作用群的分类空间的上同调环上的环，而且是其上的代数。证明了环面流形（即紧致光滑环面簇）同构为簇的充要条件是它们的等变上同调代数是弱同构的。我们还证明了拟流形，这可以被认为是一个拓扑对应环面流形，等变同胚当且仅当其等变上同调代数是同构的。
Localization of equivariant cohomology rings of real Grassmannians
本文通过局部化方法研究实格拉斯曼流形的等变上同调环，给出加法基并计算相关不变量，并利用等变形式性推广到普通上同调。
Equivariant Elliptic Cohomology and Rigidity
复系数等变椭圆上同调由Ginzburg，Kapranov和Vasserot公理化地定义，并由Grojnowski构造。给出了S^1-等变椭圆上同调的一个不变定义，并利用它给出了Witten关于椭圆亏格的刚性定理的一个完全上同调证明。我们还陈述并证明了椭圆族的一个刚性定理。
We describe the equivariant cohomology ring of rationally smooth projective embeddings of reductive groups. These embeddings are the projectivizations of reductive monoids. Our main result describes their equivariant cohomology in terms of roots, idempotents, and underlying monoid data. Also, we characterize those embeddings whose equivariant cohomology ring is obtained via restriction to the associated toric variety. Such characterization is given in terms of the closed orbits.
Equivariant cohomology and analytic descriptions of ring isomorphisms
本文考虑一类连通闭$G$ -流形，其中每个$M$在$M_G$（或$G$ -等变形式）中与零完全非同调，且具有非空的有限不动点集，其中$G={\Bbb Z}_2$ .借助于等变指标，我们给出了这类$G$ -流形的等变上同调的代数描述，从而得到了这类$G$ -流形的等变上同调环之间的环同构的解析描述，以及这两个$G$ -流形的等变上同调环同构的充要条件.这也导致我们分析有多少等变上同调环同构等$G$ -流形在2-和3-维的情况下。
We study the multiplication and comultiplication in equivariant cohomology of Sato Grassmannian
We determine the $T$-equivariant integral cohomology of $F_4/T$ combinatorially by the GKM theory, where T is a maximal torus of the exceptional Lie group $F_4$ and acts on $F_4/T$ by the left multiplication.
We extend the work of Allday-Franz-Puppe on syzygies in equivariant cohomology from tori to arbitrary compact connected Lie groups G. In particular, we show that for a compact orientable G-manifold X the analogue of the Chang-Skjelbred sequence is exact if and only if the equivariant cohomology of X is reflexive, if and only if the equivariant Poincare pairing for X is perfect. Along the way we establish that the equivariant cohomology modules arising from the orbit filtration of X are Cohen-Macaulay. We allow singular spaces and introduce a Cartan model for their equivariant cohomology. We al…
The chiral equivariant cohomology contains and generalizes the classical equivariant cohomology of a manifold M with an action of a compact Lie group G. For any simple G, there exist compact manifolds with the same classical equivariant cohomology, which can be distinguished by this invariant. When M is a point, this cohomology is an interesting conformal vertex algebra whose structure is still mysterious. In this paper, we scratch the surface of this object in the case G=SU(2).
The Springer variety of type $A$ associated to a nilpotent operator on $\mathbb{C}^n$ in Jordan canonical form admits a natural action of the $\ell$-dimensional torus $T^{\ell}$ where $\ell$ is the number of the Jordan blocks. We give a presentation of the $T^{\ell}$-equivariant cohomology ring of the Springer variety through an explicit construction of an action of the $n$-th symmetric group on the $T^{\ell}$-equivariant cohomology group. The $T^{\ell}$-equivariant analogue of so called Tanisaki's ideal will appear in the presentation.
Reconstructing the orbit type stratification of a torus action from its equivariant cohomology
本文研究了如何从紧空间上环面作用的有理等变上同调代数中提取轨道类型分层信息，证明了其编码了分支元素子偏序集，并在等变形式及光滑条件下揭示了流形等变上同调对各分层信息的编码机制。
In this article we study the equivariant elliptic cohomology of complex toric varieties. We prove a partial reconstruction theorem showing that equivariant elliptic cohomology encodes considerable non-trivial information on the equivariant 1-skeleton of a toric variety X (although it stops short of being a complete invariant of its GKM graphs). Elliptic cohomology is supposed to encode higher categorical geometric data, and proposals have been made linking elliptic cocycles to categorified bundles. In particular, contrary to ordinary cohomology and K-theory, elliptic cohomology is expected not…
An introduction to equivariant cohomology and homology, following Goresky, Kottwitz, and MacPherson
本文利用Goresky，Kottwitz和MacPherson的方法介绍了等变上同调和同调。当群G适当地作用在簇X上时，X的等变上同调可以利用X上G-轨道骨架的组合数据来计算。给出了等变上同调的几何定义和传统定义。我们包括一个讨论的矩映射和一个算法，找到一组发电机的等变上同调的X。文中给出了许多算例和显式计算。
We compute the complete RO(G)-graded coefficients of "ordinary" cohomology with coefficients in Z/2 for G=(Z/2)^n.
Equivariant Morse-Bott cohomology through stabilization
本文通过稳定化技术研究等价不变的莫尔斯-博特上同调，证明小扰动产生稳定不变函数，并利用通用度量实现横截性和定向性假设。
The geometry of the local cohomology filtration in equivariant bordism
等变同伦理论中的局部上同调技术，由John Greenlees引入，可以应用于通过其他等变数据来理解分类空间的同调。本文将局部上同调滤子与族滤子联系起来。通过这样做，我们可以识别几何编码的局部上同调过滤设置的等变边。自然产生的结构分析本地化K-理论机器由于Atiyah和Segal，我们审查。
We introduce a Bredon motivic cohomology theory for smooth schemes defined over a field and equipped with an action by a finite group. These cohomology groups are defined for finite dimensional representations as the hypercohomology of complexes of equivariant correspondences in the equivariant Nisnevich topology. We generalize the theory of presheaves with transfers to the equivariant setting and prove a Cancellation Theorem.
We sketch a quick and dirty geometric approach to the Tate-Swan cohomology of equivariant spectra, illustrating it with conjectural applications to Atiyah-Segal $K$-theory of circle actions, and a possible geometric model for the topological cyclic homology of the sphere spectrum.
The equivariant cohomology for actions of compact connected abelian groups and elementary abelian p-groups have been widely studied in the last decades. We study some of these results on actions of finite cyclic groups over a field of positive characteristic. In particular, we study the module structure of the equivariant cohomology over the cohomology of the classifying space and we provide a criterion for freeness over this ring and the polynomial subring of it. We apply these results to canonical actions of finite cyclic groups on polyhedral products arising from the boundary of a polygo
We consider closed manifolds, which occur as intersections of products of spheres of the same dimension with certain hyperplanes. Among those are the so called (big) polygon- and chain spaces. The equivariant cohomology with respect to natural actions of 2-tori is calculated and related to the notion of syzygy. It turns out that the equivariant cohomology module of these manifolds is often torsion free, but not free over the cohomology of the group. Coefficients are taken in the field with two elements.
Koszul duality and equivariant cohomology for tori
设T为环面。我们证明了Koszul对偶可以用来计算拓扑T-空间的等变上同调以及泛T-丛的拉回的上同调。新的特点是不再对空间作进一步的假设，而且系数环可以是任意的。这特别给出了一个任意系数的T-空间的等变上同调的Cartan型模型。我们的方法也适用于相交同调。
In this paper, we calculate the $RO(G)$-graded coefficients of $H\underline{\mathbb{Z}}$, the Eilenberg-MacLane spectrum of constant Mackey functor for quaternion group $Q_8$.
Equivariant homology and cohomology of groups
当一个单独的群“gamma”作用在G和A上时，我们给出并研究了系数在gamma-等变G-模A中的群G的群（上）同调的等变理论，推广了经典的群的Eilenberg-MacLane（上）同调.建立了拓扑空间与等变上同调的关系，并给出了它在代数K理论中的应用。
In this paper, we prove that the orbit space B and the Euler class of an action of the circle S^1 on X determine both the equivariant intersection cohomology of the pseudomanifold X and its localization. We also construct a spectral sequence converging to the equivariant intersection cohomology of X whose third term is described in terms of the intersection cohomology of B.
Let $C_2$ denote the cyclic group of order two. Given a manifold with a $C_2$-action, we can consider its equivariant Bredon $RO(C_2)$-graded cohomology. In this paper, we develop a theory of fundamental classes for equivariant submanifolds in $RO(C_2)$-graded cohomology in constant $\mathbb{Z}/2$ coefficients. We show the cohomology of any $C_2$-surface is generated by fundamental classes, and these classes can be used to easily compute the ring structure. To define fundamental classes we are led to study the cohomology of Thom spaces of equivariant vector bundles. In general the cohomology o…
In this paper, we prove some computational results about equivariant cohomology over the cyclic group $C_{p^n}$ of prime power order. We show that there is an inductive formula when the dimension of the $C_p$-fixed points of the grading is large. Among other calculations, we also show the existence of non-trivial extensions when $n\geq 3$.
Let X be a "nice" space with an action of a torus T. We consider the Atiyah-Bredon sequence of equivariant cohomology modules arising from the filtration of X by orbit dimension. We show that a front piece of this sequence is exact if and only if the H^*(BT)-module H_T^*(X) is a certain syzygy. Moreover, we express the cohomology of that sequence as an Ext module involving a suitably defined equivariant homology of X. One consequence is that the GKM method for computing equivariant cohomology applies to a Poincare duality space if and only if the equivariant Poincare pairing is perfect.
We show the compatibility of the differential geometric and the topological construction of equivariant characteristic classes for compact Lie groups. Our analysis motivates a differential geometric construction for equivariant characteristic classes in the non-compact case. This compatibility is generally assumed and used in various cases, but there is only a proof for compact connected Lie groups in the literature, see the work of Raoul Bott and Loring Tu. Our proof applies and generalizes ideas of Johan Dupont and Ezra Getzler.
When a torus acts on a compact oriented manifold with isolated fixed points, the equivariant localization formula of Atiyah--Bott--Berline--Vergne converts the integral of an equivariantly closed form to a finite sum over the fixed points, providing a powerful tool for computing integrals on a manifold. This article seeks to give an accessible exposition of the equivariant localization formula.
The $C_2$-equivariant ordinary cohomology of complex quadrics III: Exceptional cases
本文为$C_2$等变复二次曲面系列终篇，完成不动点集分量超2的光滑对称二次曲面等变普通上同调计算，推导对应格拉斯曼流形结果，证明了三维射影空间三次曲面27条直线结论的等变细化。
We develop a theory of syzygies in equivariant cohomology for tori as well as $p$-tori and coefficients in $\mathbb{F}_p$. A noteworthy feature is a new algebraic approach to the partial exactness of the Atiyah-Bredon sequence, which also covers all instances considered so far.
In this article we introduce flag Bott manifolds of general Lie type as the total spaces of iterated flag bundles. They generalize the notion of flag Bott manifolds and generalized Bott manifolds, and admit nice torus actions. We calculate the torus equivariant cohomology rings of flag Bott manifolds of general Lie type.
We study the $S_n$-equivariant log-concavity of the cohomology of flag varieties, also known as the coinvariant ring of $S_n$. Using the theory of representation stability, we give computer-assisted proofs of the equivariant log-concavity in low degrees and high degrees and conjecture that it holds for all degrees. Furthermore, we make a stronger unimodal conjecture which implies the equivariant log-concavity.
We completely calculate the $RO(G)$-graded coefficients of ordinary equivariant cohomology where $G$ is the dihedral group of order $2p$ for a prime $p>2$ both with constant and Burnside ring coefficients. The authors first proved it for $p=3$ and then the second author generalized it to arbitrary $p$. These are the first such calculations for a non-abelian group.
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。