相关论文: On free actions of discrete quantum groups

Let $G$ be a connected Lie group of rank one. In this paper the existence of free actions of group $G$ on spheres, real projective spaces and lens spaces has been studied. Most of the results have been obtained for finitistic spaces with…

We show that a continuous action of a quantum semigroup $\mathcal{S}$ on a finite quantum space (finite dimensional $\mathrm{C}^*$-algebra) preserving a faithful state comes from a continuous action of the quantum Bohr compactification…

Given an action of a Compact Quantum Group (CQG) on a finite dimensional Hilbert space, we can construct an action on the associated Cuntz algebra. We study the fixed point algebra of this action, using Kirchberg classification results.…

We show that any action of a finite group on a finitely presentable group arises as the action of the group of self-homotopy equivalences of a space on its fundamental group. In doing so, we prove that any finite connected (abstract)…

We show that if G is an infinitely generated locally (polycyclic-by-finite) group with cohomology almost everywhere finitary, then every finite subgroup of G acts freely and orthogonally on some sphere.

Ellis's "functional approach" allows one to obtain proper compactifications of a topological group $G$ if $G$ can be represented as a subgroup of the homeomorphism group of a space $X$ in the topology of pointwise convergence and $G$-space…

We provide a smoothening criterion for group actions on manifolds by singular diffeomorphisms. We prove that if a countable group $\Gamma$ has the fixed point property FW for walls (e.g. if it has property (T)), every aperiodic action of…

We study algebraic properties on a group G such that if the discrete group G has these properties then every locally compact shift continuous topology on G with adjoined zero is either compact, or discrete. We introduce electorally flexible…

We prove quantum ergodicity for certain orthonormal bases of $L^2(\mathbb{S}^2)$, consisting of joint eigenfunctions of the Laplacian on $\mathbb{S}^2$ and the discrete averaging operator over a finite set of rotations, generating a free…

A generalized moment map is proposed for arbitrary symplectic actions of compact connected Lie groups on closed symplectic manifolds, in the spirit of the circle -valued maps introduced by D. McDuff in the case of non-Hamiltonian circle…

We study finite abelian group actions on weakly Lefschetz cohomologically symplectic (WLS) manifolds, a collection of manifolds that includes all compact connected Kaehler manifolds. We prove that for any WLS manifold $X$ there exists a…

We introduce and systematically study the notion of Rokhlin dimension (with and without commuting towers) for compact group actions on $C^*$-algebras. This notion generalizes the one introduced by Hirshberg, Winter and Zacharias for finite…

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 prove a compactness result for classes of actions of many small categories on quantum compact metric spaces by Lipschitz linear maps, for the topology of the covariant Gromov-Hausdorff propinquity. In particular, our result applies to…

Ancel, Dobrowolski, and Grabowski (Studia Math., 1994) proved that every countable discrete subgroup of the additive group of a normed space is free Abelian, hence isomorphic to the direct sum of a certain number of copies of the additive…

The purpose of this paper is to investigate torsion-free groups which act properly and cocompactly on CAT(0) metric spaces which have isolated flats, as defined by Hruska. Our approach is to seek results analogous to those of Sela,…

We prove an analogue of the Baum-Connes conjecture for free orthogonal quantum groups. More precisely, we show that these quantum groups have a $ \gamma $-element and that $ \gamma = 1 $. It follows that free orthogonal quantum groups are $…

The Guillemin-Sternberg conjecture states that "quantisation commutes with reduction" in a specific technical setting. So far, this conjecture has almost exclusively been stated and proved for compact Lie groups $G$ acting on compact…

We introduce the {\it Ellis semigroup} of a nonautonomous discrete dynamical system $(X,f_{1,\infty})$ when $X$ is a metric compact space. The underlying set of this semigroup is the pointwise closure of $\{f\sp{n}_1 \, |\, n\in…

We study smooth locally free actions of ${\mathbb R}^n$ on manifolds $M$ of dimension $n+1$. We are interested in compact orbits and in compact actions: actions with all orbits compact. Given a compact orbit in a neighborhood of compact…