Quasi-isometry invariance of group splittings


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.


Panos Papasoglu

Mathematics Department, National and Capodistrian University of Athens, Athens, Greece