2008/07/13 by Pierre de la Harpe, de la Harpe, Pierre
Mathematics · #22D05 #22E25 #22E40 #Advanced Algebra and Geometry #Advanced Operator Algebra Research #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:22D05 #msc:22E25 #msc:22E40
paper · pdf · doi:10.48550/arxiv.0807.2030
12 pages
openalex publication_date 2008/07/13 · arxiv created 2008/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \citeBrHK. 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 \citeBrHK, and are not intended for publication.