Related papers: Large scale geometry of homeomorphism groups

We use the reflection group trick to glue manifolds with corners that are Borel-Serre compactifications of locally symmetric spaces of noncompact type and obtain aspherical manifolds. We call these \emph{piecewise locally symmetric}…

Let M be a closed connected oriented manifold admitting a non-zero degree map to a nilmanifold. In the first part of the paper we study effective finite group actions on M. In particular, we prove that Homeo(M) is Jordan, we bound the…

We construct a geometric model for the mapping class group M of a non-exceptional oriented surface of finite type and use it to show that the action of M on the compact Hausdorff space of complete geodesic laminations is topologically…

We study groups of homeomorphic bijections on spaces that are finite unions of compact connected linearly ordered subsets. We prove that all such groups when endowed with the topology of point-wise convergence are topological groups. }

We characterize maps between $n$-dimensional N\"obeling manifolds that can be approximated by homeomorphisms.

If G is a (connected) complex Lie Group and Z is a generalized flag manifold for G, the the open orbits D of a (connected) real form G_0 of G form an interesting class of complex homogeneous spaces, which play an important role in the…

We study analogues of Cartan decompositions of Lie groups for totally disconnected locally compact groups. It is shown using these decompositions that a large class of totally disconnected locally compact groups acting on trees and…

Let M be a closed simply connected n-manifold of positive sectional curvature. We determine its homeomorphism or homotopic type if M also admits an isometric elementary p-group action of large rank. Our main results are: There exists a…

Given a group $G$ of automorphisms of a matroid $M$, we describe the representations of $G$ on the homology of the independence complex of the dual matroid $M^*$. These representations are related with the homology of the lattice of flats…

We show that, given any finite dimensional, connected, compact metric space Z, there exists a group G acting geometrically on two CAT(0) spaces X and Y, a G-equivariant quasi-isometry f from X to Y, and a geodesic ray c in X, such that the…

We study the topological full group of ample groupoids over locally compact spaces. We extend Matui's definition of the topological full group from the compact, to the locally compact case. We provide two general classes of groupoids for…

We describe all connected components of the space of hyperbolic Gorenstein quasi-homogeneous surface singularities. We prove that any connected component is homeomorphic to a quotient of R^d by a discrete group.

This sequel to our previous paper [MS11b] continues the study of topological contact dynamics and applications to contact dynamics and topological dynamics. We provide further evidence that the topological automorphism groups of a contact…

Let G be a finitely presented group, and G' its commutator subgroup. Let C be the Cayley graph of G' with all commutators in G as generators. Then C is large scale simply connected. Furthermore, if G is a torsion-free nonelementary…

We prove a structure theorem for compact aspherical Lorentz manifolds with abundant local symmetry. If M is a compact, aspherical, real-analytic, complete Lorentz manifold such that the isometry group of the universal cover has semisimple…

We introduce a topology on the space of all isomorphism types represented in a given class of countable models, and use this topology as an aid in classifying the isomorphism types. This mixes ideas from effective descriptive set theory and…

Given a locally compact Polish space X, a necessary and sufficient condition for a group G of homeomorphisms of X to be the full isometry group of (X,d) for some proper metric d on X is given. It is shown that every locally compact Polish…

We give a short, mostly elementary and self-contained proof of the classical result that the groups of diffeomorphisms, homeomorphisms, and homotopy equivalences of a surface have the same group of connected components.

Let $F$ be a non-singular foliation on the plane with all leaves being closed subsets, $H^{+}(F)$ be the group of homeomorphisms of the plane which maps leaves onto leaves endowed with compact open topology, and $H^{+}_{0}(F)$ be the…

In this paper, we study some properties of self-homeomorphisms on the Mac\'ias topology over $\mathbb{N}$, and we demonstrate that this space is not topologically rigid.