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The Chabauty space of closed subgroups of the three-dimensional Heisenberg group

Abstract:

When equipped with the natural topology first defined by Chabauty, the closed subgroups of a locally compact group $G$ form a compact space $\Cal C(G)$. We analyse the structure of $\Cal C(G)$ for some low-dimensional Lie groups, concentrating mostly on the 3-dimensional Heisenberg group $H$. We prove that $\Cal C(H)$ is a 6-dimensional space that is path--connected but not locally connected. The lattices in $H$ form a dense open subset $\Cal L(H) \subset \Cal C(H)$ that is the disjoint union...

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Publication status:
Published

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Publisher copy:
10.2140/pjm.2009.240.1

Authors


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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Harpe, PDL More by this author
Kleptsyn, V More by this author
Journal:
PACIFIC JOURNAL OF MATHEMATICS
Volume:
240
Issue:
1
Pages:
1-48
Publication date:
2007-11-23
DOI:
ISSN:
0030-8730
URN:
uuid:79560fe6-7544-43dc-8add-b76de4fccb09
Source identifiers:
30792
Local pid:
pubs:30792
Language:
English
Keywords:

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