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Panos Papasoglu

Group splittings and asymptotic topology

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.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2007, 01/2007
Pages: 1 - 16

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