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Length functions, curvature, and the dimension of discrete groups

Abstract:
We work with the class of groups that act properly by semisimple isometrics on complete CAT(0) spaces. Define dimss Γ to be the minimal dimension in which Γ admits such an action. By examining the nature of translation length functions we show that there exist finitely-presented, torsion-free groups Γ for which dimss Γ is greater than the cohomological dimension of Γ. We also show that dimss Γ can decrease when one passes to a subgroup of finite index.
Publication status:
Published

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Publisher copy:
10.4310/MRL.2001.v8.n4.a14

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Institution:
University of Oxford
Department:
Oxford, MPLS, Mathematical Inst
Journal:
MATHEMATICAL RESEARCH LETTERS
Volume:
8
Issue:
4
Pages:
557-567
Publication date:
2001-07-05
DOI:
EISSN:
1945-001X
ISSN:
1073-2780
URN:
uuid:55cd6017-f36e-468a-bdb4-c0040c040e33
Source identifiers:
11293
Local pid:
pubs:11293
Language:
English

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