Related papers: Connectivity of the coset poset

The pro-\'etale fundamental group of a scheme, introduced by Bhatt and Scholze, generalizes the usual \'etale fundamental group $\pi_1^{\mathrm{et}}$ defined in SGA1 and leads to an interesting class of "geometric coverings" of schemes,…

In this paper, we study the simplex faces of the order polytope $\mathcal{O}(P)$ and the chain polytope $\mathcal{C}(P)$ of a finite poset $P$. We show that, if $P$ can be recursively constructed from $\mathbf{X}$-free posets using disjoint…

Let G be a group and let M be a CAT(0) proper metric space (e.g. a simply connected complete Riemannian manifold of non-positive sectional curvature or a locally finite tree). Isometric actions of G on M are (by definition) points in the…

We show that for any finitely presented group $G$, there is a simply connected closed 4-manifold containing an infinite family of topologically isotopic but smoothly inequivalent 2-links whose 2-link group is $G$. We also show that, if $G$…

This paper expands on and refines some known and less well-known results about the finite subset spaces of a simplicial complex $X$ including their connectivity and their top homology groups. It also discusses the inclusion of the…

We study the congruence lattice of the poset of regions of a hyperplane arrangement, with particular emphasis on the weak order on a finite Coxeter group. Our starting point is a theorem from a previous paper which gives a geometric…

We prove that a connected simplicial complex is uniquely determined by its complex of discrete Morse functions. This settles a question raised by Chari and Joswig. In the 1-dimensional case, this implies that the complex of rooted forests…

The topological coset model appraoch to non-critical string models is summarized. The action of a topological twisted ${G\over H}$ coset model ($rank\ H = rank\ G$) is written down. A ``topological coset algebra" is derived and compared…

Let G be a finite group and H a normal subgroup such that G/H is cyclic. Given a conjugacy class g^G of G we define its centralizing subgroup to be HC_G(g). Let K be such that H\le K\le G. We show that the G-conjugacy classes contained in K…

We study two different objects attached to an arbitrary quadrangulation of a regular polygon. The first one is a poset, closely related to the Stokes polytopes introduced by Baryshnikov. The second one is a set of some paths configurations…

There are two approaches to the homotopy theory of simplicial (pre-)sheaves. One developed by Joyal and Jardine works for all sites but produces a model structure which is not finitely generated even in the case of sheaves on a Noetherian…

We examine properties of generic automorphisms of the random poset, with the goal of explicitly characterizing them. We associate to each automorphism an auxiliary first-order structure, consisting of the random poset equipped with an…

For a compact Lie group G we show that if the representing spectrum for Borel cohomology generates its category of modules if G is connected. For a closed subgroup H of G we consider the map C^*(BG)--->C^*(BH) and establish the sense in…

A number of proposals with differing predictions (e.g. Borel group cohomology, oriented cobordism, group supercohomology, spin cobordism, etc.) have been made for the classification of symmetry protected topological (SPT) phases. Here we…

We study the computational problem of checking whether a quantified conjunctive query (a first-order sentence built using only conjunction as Boolean connective) is true in a finite poset (a reflexive, antisymmetric, and transitive directed…

There are a large number of theorems detailing the homological properties of the Stanley--Reisner ring of a simplicial complex. Here we attempt to generalize some of these results to the case of a simplicial poset. By investigating the…

Let $p$ be a branched covering of a Riemann surface to the Riemann sphere $\mathbb{P}^1$, with branching set $B \subset \mathbb{P}^1$. We define the complexity of $p$ as infinity, if $\mathbb{P}^1 \setminus B$ does not admit a hyperbolic…

Let $A$ be either a simplicial complex $K$ or a small category $\mathcal C$ with $V(A)$ as its set of vertices or objects. We define a twisted structure on $A$ with coefficients in a simplicial group $G$ as a function $$ \delta\colon…

We consider a weakly coupled gauge theory where charged particles all have large gaps (ie no Higgs condensation to break the gauge "symmetry") and the field strength fluctuates only weakly. We ask what kind of topological terms can be added…

It was proven by Gonz\'alez-Meneses, Manch\'on and Silvero that the extreme Khovanov homology of a link diagram is isomorphic to the reduced (co)homology of the independence simplicial complex obtained from a bipartite circle graph…