Group splittings and asymptotic topology

Details Group splittings and asymptotic topology Group splittings and asymptotic topology

2002-01-31

arxiv.org/abs/math/0201312v1

Mathematics

Group Theory

14 pages

Scientific paper

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.

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