ar X iv : m at h / 02 01 31 2 v 1 [ m at h . G R ] 3 1 Ja n 20 02 GROUP SPLITTINGS AND ASYMPTOTIC TOPOLOGY
نویسندگان
چکیده
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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