Volume 10, issue 3 (2010)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
L'espace des sous-groupes fermés de $\mathbb{R} \times \mathbb{Z}$

Thomas Haettel

Algebraic & Geometric Topology 10 (2010) 1395–1415
Abstract

The space of closed subgroups of a locally compact topological group is endowed with a natural topology, called the Chabauty topology. We completely describe the space of closed subgroups of the group × (and of its dual ×), which is highly nontrivial : for example, its fundamental group contains the fundamental group of the Hawaiian earrings, hence is uncountable.

L’espace des sous-groupes fermés d’un groupe topologique localement compact est muni d’une topologie naturelle, appelée topologie de Chabauty. Nous décrivons complètement l’espace des sous-groupes fermés du groupe × (et de son dual ×), lequel est hautement non trivial : par exemple, son groupe fondamental contient le groupe fondamental des anneaux Hawaïens, et est donc non dénombrable.

Keywords
Chabauty, space of closed subgroups, Hawaiian earrings, espace des sous-groupes fermés
Mathematical Subject Classification 2000
Primary: 22B99, 22D05
Secondary: 20F65, 57M07
References
Publication
Received: 19 December 2008
Revised: 20 May 2009
Accepted: 8 July 2009
Published: 25 June 2010
Authors
Thomas Haettel
École Normale Supérieure, DMA UMR 8553 CNRS
45 rue d’Ulm, 75005 Paris
France