Related papers: Representations of polygons of finite groups

We prove that many relatively hyperbolic groups obtained by relative strict hyperbolization admit a cocompact action on a CAT(0) cubical complex. Under suitable assumptions on the peripheral subgroups, these groups are residually finite and…

We construct a projective variety with discrete, non-finitely generated automorphism group. As an application, we show that there exists a complex projective variety with infinitely many non-isomorphic real forms.

These are lectures on discrete groups of isometries of complex hyperbolic spaces, aimed to discuss interactions between the function theory on complex hyperbolic manifolds and the theory of discrete groups.

The orthogonal groups are a series of simple Lie groups associated to symmetric bilinear forms. There is no analogous series associated to symmetric trilinear forms. We introduce an infinite dimensional group-like object that can be viewed…

This is an expository book on unitary representations of topological groups, and of several dual spaces, which are spaces of such representations up to some equivalence. The most important notions are defined for topological groups, but a…

In this article we introduce order preserving representations of fundamental groups of surfaces into Lie groups with bi-invariant orders. By relating order preserving representations to weakly maximal representations, introduced in…

We analyze the abstract representations of the groups of rational points of even-dimensional quasi-split special unitary groups associated with quadratic field extensions. We show that, under certain assumptions, such representations have a…

We show that the algebraic fundamental group of a smooth projective curve over a finite field admits a finite topological presentation where the number of relations does not exceed the number of generators.

We describe the quasi-isometric classification of fundamental groups of irreducible non-geometric 3-manifolds which do not have "too many" arithmetic hyperbolic geometric components, thus completing the quasi-isometric classification of…

We give the first examples of closed fibered hyperbolic 3-manifolds whose fundamental groups are distinguished from every other finitely generated, residually finite group by their finite quotients. One of the examples is also the first…

In this paper we consider ultra-parallel complex hyperbolic triangle groups of type $[m_1,m_2,0]$, i.e. groups of isometries of the complex hyperbolic plane, generated by complex reflections in three ultra-parallel complex geodesics two of…

We construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of countably infinite amenable groups and use these representations to find explicit generating partitions…

Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the…

Let K be a fine hyperbolic graph and G be a group acting on K with finite quotient. We prove that G is exact provided that all vertex stabilizers are exact. In particular, a relatively hyperbolic group is exact if all its peripheral groups…

We prove that there is a one-one correspondence between sets of irreducible representations of a polyadic group and its Post's cover. Using this correspondence, we generalize some well-known properties of irreducible characters in finite…

We characterize dual spaces and compute hyperdimensions of irreducible representations for two classes of compact hypergroups namely conjugacy classes of compact groups and compact hypergroups constructed by joining compact and finite…

We obtain explicit formulas for the rational homotopy groups of generalised symmetric spaces, i.e., the homogeneous spaces for which the isotropy subgroup appears as the fixed point group of some finite order automorphism of the group. In…

We suggest a new approach to the study of relatively hyperbolic groups based on relative isoperimetric inequalities. Various geometric, algebraic, and algorithmic properties are discussed.

We describe and study the loci equidistant from finitely many points in the so-called complex hyperbolic geometry, i.e., in the geometry of a holomorphic $2$-ball $\Bbb B$. In particular, we show that the bisectors (= the loci equidistant…

In this note we investigate to what extent the fundamental group of a metric space can be described as the inverse limit of its discrete fundamental groups. We show that some mild conditions suffice to imply the existence of an isomorphism…