On the one-endedness of graphs of groups
Group Theory
2016-01-20 v2 Geometric Topology
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.
Keywords
Cite
@article{arxiv.1403.6452,
title = {On the one-endedness of graphs of groups},
author = {Nicholas Touikan},
journal= {arXiv preprint arXiv:1403.6452},
year = {2016}
}
Comments
Improved exposition. 17 pages, 7 figures. To appear in Pacific J. Math