Related papers: Finite group actions on Kan complexes

An action of a group on a set is oligomorphic if it has finitely many orbits of $n$-element subsets for all $n$. We prove that for a large class of groups (including all groups of finite virtual cohomological dimension and all countable…

Let $S$ be a right reversible semitopological semigroup, and let $\operatorname{LUC}(S)$ be the space of left uniformly continuous functions on $S$. Suppose that $\operatorname{LUC}(S)$ has a left invariant mean. Let $K$ be a weakly compact…

Toward the complete classification of poly-$\mathbb{Z}$ group actions on Kirchberg algebras, we prove several fundamental theorems that are used in the classification. In addition, as an application of them, we classify outer actions of…

The genus spectrum of a finite group $G$ is the set of all $g\geq 2$ such that $G$ acts faithfully and orientation-preserving on a closed compact orientable surface of genus $g$. This article is an overview of some results relating the…

Let $V$ be a finite set. Let $\mathcal{K}$ be a simplicial complex with its vertices in $V$. In this paper, we discuss some differential calculus on $V$. We construct some constrained homology groups of $\mathcal{K}$ by using the…

We study equivariant deformations of singular curves with an action of a finite flat group scheme, using a simplified version of Illusie's equivariant cotangent complex. We apply these methods in a special case which is relevant for the…

In this work, we introduce the notion of a partial action of a group on a strict monoidal category. We propose, in the context of Monoidal categories, new constructions analogous to those existing for partial group actions over an algebra…

We present a general framework for reduction of symplectic Q-manifolds via graded group actions. In this framework, the homological structure on the acting group is a multiplicative multivector field.

Recall that a pseudofree group action on a space is one whose singular set consists only of isolated points. In this paper, we classify all of the finite groups which admit pseudofree actions on S^2 x S^2. The groups turn out to be exactly…

Any compact surface supports a continuous action of the orientation preserving affine group of the real line which is fixed point free (Lima and Plante). It is generally admitted that this action can be taken smooth although it is not easy…

In this paper we study the cohomology of the geometric realization of linking systems with twisted coefficients. More precisely, given a prime $p$ and a $p$-local finite group $(S,\mathcal{F},\mathcal{L})$, we compare the cohomology of…

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid…

We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.

We generalise Atiyah and Hirzebruch's vanishing theorem for actions by compact groups on compact Spin-manifolds to possibly noncompact groups acting properly and cocompactly on possibly noncompact Spin-manifolds. As corollaries, we obtain…

We prove that every finite connected simplicial complex has the homology of the classifying space for some $\mathrm{CAT}(0)$ cubical duality group. More specifically, for any finite simplicial complex $X$, we construct a locally…

We introduce the notion of a ``sofic $\mathcal{C}$-action'' of one group on another by automorphisms, for $\mathcal{C}$ a class of groups. We show that if $\mathcal{C}$ is the class of (i) sofic, (ii) hyperlinear, (iii) linear sofic or (iv)…

We classify compact homogeneous geometries of irreducible spherical type and rank at least 2 which admit a transitive action of a compact connected group, up to equivariant 2-coverings. We apply our classification to polar actions on…

Let $K\to U(V)$ be a unitary representation of the compact Lie group $K$. Then there is a canonical moment mapping $\rho\colon V\to\mathfrak k^*$. We have the Koszul complex ${\mathcal K}(\rho,\mathcal C^\infty(V))$ of the component…

Let $\Gamma$ be a simple undirected graph on a finite vertex set and let $A$ be its adjacency matrix. Then $\Gamma$ is {\it singular} if $A$ is singular. The problem of characterising singular graphs is easy to state but very difficult to…

Let $G$ be a complex Lie group acting on a compact complex Hermitian manifold $M$ by holomorphic isometries. We prove that the induced action on the Dolbeault cohomology and on the Bott-Chern cohomology is trivial. We also apply this result…