Spaces of closed subgroups of locally compact groups
| dc.creator | de la Harpe, Pierre | |
| dc.date | 2008-07-13 | |
| dc.date | 2008-11-12 | |
| dc.date.accessioned | 2026-07-07T10:17:21Z | |
| dc.date.available | 2026-07-07T10:17:21Z | |
| dc.description | 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,} École Normale Supérieure de Lyon, June 13, 2008; and seminars at the EPFL, Lausanne, and in the Université de Rennes 1. The notes do not contain any other result than those in \cite{BrHK}, and are not intended for publication. | |
| dc.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/0807.2030 | |
| dc.identifier | http://arxiv.org/abs/0807.2030 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/173826 | |
| dc.subject | Group Theory | |
| dc.subject | 22D05; 22E25; 22E40 | |
| dc.title | Spaces of closed subgroups of locally compact groups | |
| dc.type | text |