Spaces of closed subgroups of locally compact groups

By Pierre de la Harpe. 2008

57 citations recorded by the source corpus.

The set $\Cal C(G)$ of closed subgroups of a locally compact group $G$ has a natural topology which makes it a compact space. This topology has been defined in various contexts by Vietoris, Chabauty, Fell, Thurston, Gromov, Grigorchuk, and many others. The purpose of the talk was to describe the space $\Cal C(G)$ first for a few elementary examples, then for $G$ the complex plane, in which case $\Cal C(G)$ is a 4--sphere (a result of Hubbard and Pourezza), and finally for the 3--dimensional Heisenberg group $H$, in which case $\Cal C(H)$ is a 6--dimensional singular space recently investigated by Martin Bridson, Victor Kleptsyn and the author \cite{BrHK}. These are slightly expanded notes prepared for a talk given at several places: the Kortrijk workshop on {\it Discrete Groups and Geometric Structures, with Applications III,} May 26--30, 2008; the {\it Tripode 14,} \'Ecole Normale Sup\'erieure de Lyon, June 13, 2008; and seminars at the EPFL, Lausanne, and in the Universit\'e de Rennes 1. The notes do not contain any other result than those in \cite{BrHK}, and are not intended for publication.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/cb0c9262b64bf66fe6076e6d87f72f4af492e14e

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the growth of $L^2$-invariants for sequences of lattices in Lie groups (2012, background): “We refer the reader to [68] (and also to [62]) for more information on the topology of Chabauty spaces.”