Related papers: A survey of topological Zimmer's program

This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.

We prove that every topological action of a countable group on a metrizable space can be realized as a bi-Lipschitz action with respect to some compatible metric. This extends a result due to U. Hamenst\"{a}dt regarding finitely generated…

In this note, we lay the groundwork for a new approach to the problem of group-signature classification of group actions on closed Riemann surfaces. This new approach first focuses on analyzing the low level arithmetic conditions on…

This article contains an overview of the results of the author in a field of algebraic topology used in computer science. The relationship between the cubical homology groups of generalized tori and homology groups of partial trace monoid…

Topological groupoids admit various types of morphisms. We push these notions to the level of continuous groupoid actions to obtain various types of groupoid action morphisms. Some dynamical properties and their relation to these morphisms…

We construct membrane homology groups $\h(M)$ associated with each compact connected oriented smooth manifold, and show that $\h(M)$ is matrix graded algebra.

The theme of this survey is that subgroups of the mapping class group of a finite type surface S can be studied via the geometric/dynamical properties of their action on the Thurston compactification of the Teichmuller space of S, just as…

The article is devoted to the investigation of groups of diffeomorphisms and loops of manifolds over ultra-metric fields of zero and positive characteristics. Different types of topologies are considered on groups of loops and…

In this paper we generalize to coisotropic actions of compact Lie groups a theorem of Guillemin on deformations of Hamiltonian structures on compact symplectic manifolds. We show how one can reconstruct from the moment polytope the…

Let $\Gamma$ be a finitely generated group which admits an action by homeomorphisms on a compact metrizable space $X$. We show that there is a metric on $X$ defining the original topology such that for this metric, the action is by…

We prove results toward classifying compact Lorentz manifolds on which Heisenberg groups act isometrically. We give a general construction, leading to a new example, of codimension-one actions--those for which the dimension of the…

The standard P. A. Smith theory of p-group actions on spheres, disks, and euclidean spaces is extended to the case of p-group actions on tori (i.e., products of circles) and coupled with topological surgery theory to give a complete…

We propose some problems on the classification of toric manifolds from the viewpoint of topology and survey related results.

We survey some results on toric topology.

This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…

In this article we describe relations of the topology of closed 1-forms to the group theoretic invariants of Bieri-Neumann-Strebel-Renz. Starting with a survey, we extend these Sigma invariants to finite CW- complexes and show that many…

It is a well known result in the covering groups that a subgroup $G$ of the fundamental group at the identity of a semi-locally simply connected topological group determines a covering morphism of topological groups with characteristic…

In this paper, we study a point-hyper plane incidence theorem in matrix rings, which generalizes all previous works in literature of this direction.

We study the model theory of covers of groups definable in o-minimal structures. This includes the case of covers of compact real Lie groups. In particular we study categoricity questions, pointing out some notable differences with the case…

We study several properties of expansive group actions on metric spaces and obtain relation between expansivity for subgroup and group actions. Through counter examples necessity of hypothesis are justified. We also study expansivity of…