相关论文: Actions of SL(n,Z) on homology spheres

We study finite group actions on smooth manifolds of the form $M\#\Sigma$, where $\Sigma$ is an exotic $n$-sphere and $M$ is a closed aspherical space form. We give a classification result for free actions of finite groups on $M\#\Sigma$…

We use methods from the cohomology of groups to describe the finite groups which can act freely and homologically trivially on closed 3-manifolds which are rational homology spheres.

We prove that if a finite group $G$ has a representation with fixity $f$, then it acts freely and homologically trivially on a finite CW-complex homotopy equivalent to a product of $f+1$ spheres. This shows, in particular, that every finite…

We use the notion of fixity for representations of finite groups to construct free and smooth actions on products of spheres. In particular we show that a finite p-group (for p>3) will act freely and smoothly on a product of two spheres if…

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

A hyperbolic group acts by homeomorphisms on its Gromov boundary. We show that if this boundary is a topological n-sphere the action is topologically stable in the dynamical sense: any nearby action is semi-conjugate to the standard…

The only finite nonabelian simple group acting on a homology 3-sphere - necessarily non-freely - is the dodecahedral group $\Bbb A_5 \cong {\rm PSL}(2,5)$ (in analogy, the only finite perfect group acting freely on a homology 3-sphere is…

All the actions considered here are (real) analytic. Consider a subgroup of finite index of SL(n, Z). We prove, in particular, the (global) homotopical rigidity, for both its standard affine action on the torus of dimension n > 2, and its…

The author proposes a method for investigating actions of finite groups on aspherical spaces. Complete homotopy classification of free actions of finite groups on aspherical spaces is obtained. Also there are some results about non-free…

Let $p>3$ be a prime. We show that if $G$ is a finite group with $p$-rank equal to 2, then $G$ involves $Qd(p)$ if and only if $G$ $p'$-involves $Qd(p)$. This allows us to use a version of Glauberman's ZJ-theorem to give a more direct…

In this paper we study smooth orientation-preserving free actions of the cyclic group $\mathbb Z/m$ on a class of $(n-1)$-connected $2n$-manifolds, $\sharp g (S^n \times S^n)\sharp \Sigma$, where $\Sigma$ is a homotopy $2n$-sphere. When…

The main result is a classification of smooth actions of $SL(n,{\bf R})$, $n \geq 3$, or connected groups locally isomorphic to it, on closed $n$-manifolds, extending a theorem of Uchida. We construct new exotic actions of $SL(n,{\bf Z})$…

Let $\mathrm{SL}_{n}(\mathbb{Z})$ $(n\geq 3)$ be the special linear group and $M^{r}$ be a closed aspherical manifold. It is proved that when $r<n,$ a group action of $\mathrm{SL}_{n}(\mathbb{Z})$ on $M^{r}$ by homeomorphisms is trivial if…

In this paper we show that most rank two groups act freely on a finite homotopy product of two spheres. This makes new progress on a conjecture by Benson and Carlson which states that a finite group G acts freely on a finite complex with…

We obtain a sufficient and necessary condition for a finite group to act effectively on a closed flat manifold. Let \ $G=E_{n}(R)$, $EU_{n}(R,\Lambda ),$ $\mathrm{SAut}(F_{n})$ or $\mathrm{SOut}(F_{n}).$ As applications, we prove that when…

We consider orientation-preserving actions of a finite group G on the 3-sphere S^3 (and also on Euclidean space R^3). By the geometrization of finite group actions on 3-manifolds, if such an action is smooth then it is conjugate to an…

In this series of two articles, we prove that every action of a finite group $G$ on a finite and contractible $2$-complex has a fixed point. The proof goes by constructing a nontrivial representation of the fundamental group of each of the…

An analog of the Baumslag-Solitar group BS(1,k) naturally acts on the sphere by conformal transformations. The action is not locally rigid in higher dimension, but exhibits a weak form of local rigidity. More precisely, any perturbation…

We develop a new structural result for cohomogeneity one actions on (not necessarily irreducible) symmetric spaces of noncompact type and arbitrary rank. We apply this result to classify cohomogeneity one actions on SL(n,R)/SO(n), n>1, up…

For every finite-dimensional vector space V and every V-flag variety X we list all connected reductive subgroups in GL(V) acting spherically on X.