Gijs Heuts, Ieke Moerdijk
We construct a homotopy initial functor from the partition complex of a finite set $A$ to a category of trees with leaves labelled by $A$. As an application, this provides an equivalence between different bar constructions of an operad. In the differential graded case, this gives a very elementary proof of an equivalence originally due to Fresse.
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
We prove that the Bredon homology or cohomology of the partition complex with fairly general coefficients is either trivial or computable in terms of constructions with the Steinberg module. The argument involves developing a theory of Bredon homology and cohomology approximation.
Fixed points of $p$-toral groups acting on partition complexes
本文研究了$U(n)$的$p$ -带子群在酉分拆复形$\mathcal L_n$上的作用.证明了若$H\subseteq U(n)$是$p$ -群且在$\mathcal L_n$上有不可收缩的不动点，则$H$在射影酉群$U(n)/S^{1}$中的象是初等交换$p$ -群.
Matching trees for simplicial complexes and homotopy type of devoid complexes of graphs
本文将图的独立复形的同伦计算方法如分裂和匹配树推广到任意的单纯复形，并证明了它们在图的无参数化的单纯复形即单纯复形上的有效性.此外，我们还计算了弦图的控制复形的同伦类型。
A branching rule for partition complexes
设$S_n$是对称群，$Y$是$S_n$的一个Young子群.令$Π_n$是$\{1, \ldots, n\}$的分拆的复形。我们的主要结果是$Π_n$的$Y$ -等变分解.作为应用，我们通过一个Young子群得到了关于$|Π_n|$的商空间的新信息.
A matching complex of a simple graph $G$ is a simplicial complex with faces given by the matchings of $G$. The topology of matching complexes is mysterious; there are few graphs for which the homotopy type is known. Marietti and Testa showed that matching complexes of forests are contractible or homotopy equivalent to a wedge of spheres. We study two specific families of trees. For caterpillar graphs, we give explicit formulas for the number of spheres in each dimension and for perfect binary trees we find a strict connectivity bound. We also use a tool from discrete Morse theory called the \t…
Complexes of Directed Trees and Independence Complexes
复形理论的有向树是由科兹洛夫开始回答一个问题的斯坦利，后来，结果从理论所使用的巴布森和科兹洛夫在其证明的洛瓦兹猜想。我们发展了这一理论，证明了有向无圈图上的复形是可壳的。一个相关的概念是独立复形：在一个图的顶点集上构造一个单纯复形，通过包含每个独立的顶点集作为一个单纯形。证明了两个定理用于破断和胶合这样的复合物，并应用于推广Kozlov的结果。一个富有成效的限制是反Rips复形：一个度量空间的子集P是复形的顶点集，我们把P的每个子集都作为一个单纯形，其中没有一对点在距离r内。对于\mathbb{R}的任意有限子集P，反Rips复形的同伦类型是确定的.
Equivariant Trees and Partition Complexes
本文提出两个 $G$-同构划分的定义，证明其与 $G$-树在同伦上等价，并发展了 Quillen 定理的同构版本。
Nested set complexes of Dowling lattices and complexes of Dowling trees
给定一个有限群G和一个自然数n，我们研究了相应的Dowling格Q（G）的套集复形及其最近由Hultman引入的G-对称分拆的子集Q_G的复形的结构，以及G-对称系统树复形T_G的结构. Hultman证明了T_G和Q_G是同伦等价的和Cohen-Macaulay的，并确定了它们的顶同调的秩.应用Feichtner和Kozlov的建集和套集复形理论，证明了T_G实际上是被Q_G的序复形再分的.引入了Dowling树复形T（G），证明了它被Q（G）的阶复形细分，并包含T_G作为子复形.我们证明了T（G）是由T_G通过在某些子复形上连续锥化而得到的。我们显式地独立地计算了从T_G到T（G）的过程中增加了多少个同调球。
Cofiltrations of spanning trees in multiparameter persistent homology
本文提出利用生成树显式构造多参数持续同调群的生成元，引入持续生成树条件并证明其余过滤的存在性，同时推广生成复形以处理高维情形。
Directed trees in a string, real polynomials with triple roots, and chain mails
本文首先观察到两个单纯复形的无穷级数具有相同的同伦型，这两个无穷级数先验地看起来彼此没有任何关系。一个系列由双定向弦上的定向森林复形组成，而另一个系列由具有三重根的双曲多项式空间的Shapiro-Welker模型组成。我们解释这种巧合在更一般的情况下，通过找到一个明确的同伦等价复合物的有向森林双有向树，双断开复合物的树。
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…
For a finite real reflection group $W$ we use non-crossing partitions of type $W$ to construct finite cell complexes with the homotopy type of the Milnor fiber of the associated $W$-discriminant $Δ_W$ and that of the Milnor fiber of the defining polynomial of the associated reflection arrangement. These complexes support natural cyclic group actions realizing the geometric monodromy. Using the shellability of the non-crossing partition lattice, this cell complex yields a chain complex of homology groups computing the integral homology of the Milnor fiber of $Δ_W$.
In 1983 Kalai proved an incredible generalisation of Cayley's formula for the number of trees on a labelled vertex set to a formula for a class of $r$-dimensional simplicial complexes. These simplicial complexes generalise trees by means of being homologically $\Bbb Q$-acyclic. In this text we consider a different generalisation of trees to the class of pure dimensional simplicial complexes that \textit{minimally connect a vertex set} (in the sense that the removal of any top dimensional face disconnects the complex). Our main result provides an upper and lower bound for the number of these mi…
Signed Simplicial Decomposition and Overlay of n-D Polytope Complexes
多面体复形是地理信息系统（GIS）中多边形网格的任意维推广，是获取时空信息的自然概念。每个维度的复合体都有一个直接的维度独立的数据库表示，称为“关系复合体”。因此，复杂叠置是GIS中地图叠置在任意维上的相应概括。这样的叠加可以通过将单元划分为单形，将这些单形相交，并最终将它们的交点组合成所得到的叠加复合体来计算。然而，单纯形划分在大于2的维度上可能是昂贵的。在多面体复杂的情况下，覆盖/符号/单纯分解是一种替代方法。本文提出了一种忽略几何的纯组合多面体复分解。特别地，该方法也是/非凸/多面体的分解方法。几何n-D-单纯形相交，然后做了一个简化的活动集方法-一个著名的数值优化方法。然后，对单纯形交叉点进行"求和"，得到所需的叠加复合体。
A $2$-matching complex is a simplicial complex which captures the relationship between $2$-matchings of a graph. In this paper, we will use discrete Morse Theory and the Matching Tree Algorithm to prove homotopical results. We will consider a class of graphs for which the homotopy type of the $2$-matching complex transforms from a sphere to a point with the addition of leaves. We end the paper by defining $k$-matching sequences and looking at the $1$- and $2$-matching complexes of wheel graphs and perfect caterpillar graphs.
The partition number $π(K)$ of a simplicial complex $K\subset 2^{[m]}$ is the minimum integer $ν$ such that for each partition $A_1\uplus\ldots\uplus A_ν= [m]$ of $[m]$ at least one of the sets $A_i$ is in $K$. A complex $K$ is $r$-unavoidable if $π(K)\leq r$. We say that a complex $K$ is globally $r$-non-embeddable in $\mathbb{R}^d$ if for each continuous map $f: | K| \rightarrow \mathbb{R}^d$ there exist $r$ vertex disjoint faces $σ_1,\ldots, σ_r$ of $| K|$ such that $f(σ_1)\cap\ldots\cap f(σ_r)\neq\emptyset$. Motivated by the problems of Tverberg-Van Kampen-Flores type we prove several resu…
For $r\geq 1$, the $r$-independence complex of a graph $G$ is a simplicial complex whose faces are subset $I \subseteq V(G)$ such that each component of the induced subgraph $G[I]$ has at most $r$ vertices. In this article, we determine the homotopy type of $r$-independence complexes of certain families of graphs including complete $s$-partite graphs, fully whiskered graphs, cycle graphs and perfect $m$-ary trees. In each case, these complexes are either homotopic to a wedge of equi-dimensional spheres or are contractible. We also give a closed form formula for their homotopy types.
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。