Đề tài "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. 0. Introduction Stallings in [St1], [St2] shows that a finitely generated group splits over a finite group if and only if its Cayley graph has more than one end.