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Group splittings and asymptotic topology

Abstract:
It is a consequence of the theorem of Stallings on groups with many ends that splittings over finite groups are preserved by quasi-isometries. In this paper we use asymptotic topology to show that group splittings are preserved by quasi-isometries in many cases. Roughly speaking we show that splittings are preserved under quasi-isometries when the vertex groups are fundamental groups of aspherical manifolds (or more generally `coarse PD(n)-groups') and the edge groups are `smaller' than the vertex groups.
Publication status:
Published

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Publisher copy:
10.1515/CRELLE.2007.001

Authors


Journal:
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
Volume:
602
Issue:
602
Pages:
1-16
Publication date:
2002-01-31
DOI:
EISSN:
0075-4102
ISSN:
0075-4102
Source identifiers:
191448
Language:
English
Keywords:
Pubs id:
pubs:191448
UUID:
uuid:7fff9f47-d1f5-486c-ac4b-8cf489279082
Local pid:
pubs:191448
Deposit date:
2012-12-19

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