Quasi-isometry invariance of group splittings

Abstract

We show that a finitely presented one-ended group which is not commensurable to a surface group splits over a two-ended group if and only if its Cayley graph is separated by a quasi-line. This shows in particular that splittings over two-ended groups are preserved by quasi-isometries.

Authors

Panos Papasoglu

Mathematics Department
National and Capodistrian University of Athens
Athens
Greece