On the one-endedness of graphs of groups

Abstract

We give a technical result that implies a straightforward necessary and sufficient conditions for a graph of groups with virtually cyclic edge groups to be one ended. For arbitrary graphs of groups, we show that if their fundamental group is not one-ended, then we can blow up vertex groups to graphs of groups with simpler vertex and edge groups. As an application, we generalize a theorem of Swarup to decompositions of virtually free groups.

Improved exposition. 17 pages, 7 figures. To appear in Pacific J. Math

References in corpus (1)

• Krull dimension for limit groups III: Scott complexity and adjoining roots to finitely generated groups

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