Related papers: A remark about dihedral group actions on spheres

Starting from any proper action of any locally compact quantum group on any discrete quantum space, we show that its equivariant representation theory yields a concrete unitary 2-category of finite type Hilbert bimodules over the discrete…

We prove a local-to-global result for fixed points of groups acting on affine buildings (possibly non-discrete) of types $\tilde{A}_2$ or $\tilde{C}_2$. In the discrete case, our theorem establishes the corresponding special cases of a…

If $G$ is a finite $\ell$-group acting on an affine space $\mathbb{A}^n$ over a finite field $K$ of cardinality prime to $\ell$, Serre has shown that there exists a rational fixed point. We generalize this to the case where $K$ is a…

A group with a geometric action on some hyperbolic space is necessarily word hyperbolic, but on the other hand every countable group acts (metrically) properly by isometries on a locally finite hyperbolic graph. In this paper we consider…

The cyclic sieving phenomenon is a well-studied occurrence in combinatorics appearing when a cyclic group acts on a finite set. In this paper, we demonstrate a natural extension of this theory to finite abelian groups. We also present a…

We study groups acting on CAT(0) square complexes. In particular we show if Y is a nonpositively curved (in the sense of A. D. Alexandrov) finite square complex and the vertex links of Y contain no simple loop consisting of five edges, then…

We exhibit rigid rotations of spheres as distortion elements in groups of diffeomorphisms, thereby answering a question of J Franks and M Handel. We also show that every homeomorphism of a sphere is, in a suitable sense, as distorted as…

The group PGL(2) of linear transformations of the projective line acts naturally on the d-dimensional projective space P^d parametrizing configurations (`d-tuples') of points on the line. In this note we are concerned with the orbits of…

We prove two theorems of reduction of cocycles taking values in the group of diffeomorphisms of the circle. They generalise previous results obtained by the author concerning rigidity for smooth actions on the circle of Kazhdan's groups and…

Let $K\leq H$ be two finite groups and let $C\leq A$ be two finite abelian groups, with $H$ acting on $A$ as a group of isomorphisms admitting $C$ as a $K$-invariant subgroup. We study the homogeneous space $X\coloneqq\left(H\ltimes…

Let D be a division algebra with center F and degree d>2. Let K|F be any splitting field. We analyze the action of D^\times and SL_1(D) on the spherical and affine buildings that may be associated to GL_d(K) and SL_d(K), and in particular…

We construct spherical subgroups in infinite-dimensional classical groups $G$ (usually they are not symmetric and their finite-dimensional analogs are not spherical). We present a structure of a semigroup on double cosets $L\setminus G/L$…

A chiral polyhedron has a geometric symmetry group with two orbits on the flags, such that adjacent flags are in distinct orbits. Part I of the paper described the discrete chiral polyhedra in ordinary Euclidean 3-space with finite skew…

We study the action of the mapping class group on the subspace of de Rham classes in the degree-two bounded cohomology of a hyperbolic surface. In particular, we show that the only fixed nontrivial finite-dimensional subspace is the one…

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…

We classify quantum analogues of actions of finite subgroups G of SL_2(k) on commutative polynomial rings k[u,v]. More precisely, we produce a classification of pairs (H,R), where H is a finite dimensional Hopf algebra that acts inner…

In this paper, we consider the natural action of $\mathrm{SL}(3, \mathbb{H})$ on the quaternionic projective space $ \mathbb{P}_{\mathbb{H}}^2$. Under this action, we investigate limit sets for cyclic subgroups of $\mathrm{SL}(3,…

We obtain a sufficient condition for lattices in the automorphism group of a finite dimensional CAT(0) cube complex to have infinite girth. As a corollary, we get a version of Girth Alternative for groups acting geometrically: any such…

In this paper the group structure of the $p$-adic ball and sphere are studied. The dynamical system of isometry defined on invariant sphere is investigated. We define the binary operations $\oplus$ and $\odot$ on a ball and sphere…

We prove that a K\"ahler group which is cubulable, i.e. which acts properly discontinuously and cocompactly on a CAT(0) cubical complex, has a finite index subgroup isomorphic to a direct product of surface groups, possibly with a free…