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Group splittings and asymptotic topology
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Panos Papasoglu
Published/Copyright:
February 12, 2007
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.
Received: 2002-07-24
Published Online: 2007-02-12
Published in Print: 2007-01-29
© Walter de Gruyter
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