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Journal of Topology Advance Access originally published online on September 17, 2009
Journal of Topology 2009 2(3):570-588; doi:10.1112/jtopol/jtp022
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© 2009 London Mathematical Society

The space of closed subgroups of Formula is stratified and simply connected

Benoît Kloeckner

Institut Fourier — Université Grenoble 1, 100 rue des Maths, BP 74, 38402 St Martin d'Hères, France benoit.kloeckner@ujf-grenoble.fr


  Abstract

The Chabauty space of a topological group is the set of its closed subgroups, endowed with a natural topology. As soon as n > 2, the Chabauty space of Formula has a rather intricate topology and is not a manifold. By an investigation of its local structure, we fit it into a wider, but not too wild, class of topological spaces (namely, Goresky–MacPherson stratified spaces). Thanks to a localization theorem, this local study also leads to the main result of this article: the Chabauty space of Formula is simply connected for all n.

Received December 19, 2008.

2000 Mathematics Subject Classification 22E40 (primary), 57N80 (secondary)


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