Obstructions to splitting
by
Graham Niblo
University of Southampton
Coauthors: Peter Scott, Michah Sageev and Gadde Swarup

Stallings' theorem asserts that a group G splits over a finite subgroup as a non-trivial amalgamated free product or HNN extension if and only if the pair (G, {e}) has more than one end. We examine obstructions to splitting a finitely generated group over an arbitrary subgroup or class of subgroups using a recent adaptation of Sageev's cube complex associated to a group pair (G, H) with more than one end. This yields some splitting theorems which generalise results from low dimensional topology to the class of all finitely generated groups.

Date received: February 13, 2006