Related papers: Zooming in on the large-scale geometry of locally …
The purpose of this note is twofold. First, we survey results on the construction of large class groups of number fields by specialization of finite covers of curves. Then we give examples of applications of these techniques.
The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.
This paper is a survey on the {\em Zimmer program}. In it's broadest form, this program seeks an understanding of actions of large groups on compact manifolds. The goals of this survey are $(1)$ to put in context the original questions and…
This book offers to study locally compact groups from the point of view of appropriate metrics that can be defined on them, in other words to study "Infinite groups as geometric objects", as Gromov writes it in the title of a famous…
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…
This survey describes some useful properties of the local homology of abstract simplicial complexes. Although the existing literature on local homology is somewhat dispersed, it is largely dedicated to the study of manifolds, submanifolds,…
We study the large-scale geometry of mapping class groups of surfaces of infinite type, using the framework of Rosendal for coarse geometry of non locally compact groups. We give a complete classification of those surfaces whose mapping…
We examine subgroups of locally compact groups that are continuous homomorphic images of connected Lie groups and we give a criterion for being such an image. We also provide a new characterisation of Lie groups and a characterisation of…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473
We study universal groups for right-angled buildings. Inspired by Simon Smith's work on universal groups for trees, we explicitly allow local groups that are not necessarily finite nor transitive. We discuss various topological and…
We develop the fundamental theory to study cubical isometry groups as totally disconnected, locally compact groups. We show how cubical isometries are determined by their local actions and how this can be applied in explicit constructions.…
We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also…
Algebraic geometry for groups and Lie algebraic has been recently defined and studied by many authors on the purpose to study set defined by algebraic equations on abstract groups and Lie algebras. The purpose of this paper is to present a…
This is a survey article on classical groups (over arbitrary division rings) and their geometries.
We examine sufficient conditions for the dual of a topological group to be metrizable and locally compact.
This text is the preprint version of the concluding chapter for the book New Directions in Locally Compact Groups published by Cambridge University Press in the series Lecture Notes of the LMS. The recent progress on locally compact groups…
We study expressive power of continuous logic in classes of (locally compact) groups. We also describe locally compact groups which are separably categorical structures.
This is a survey on coarse geometry with an emphasis on coarse homology theories.
This (quasi-)survey addresses the quasi-isometry classification of locally compact groups, with an emphasis on amenable hyperbolic locally compact groups. This encompasses the problem of quasi-isometry classification of homogeneous…