One-ended subgroups of graphs of free groups with cyclic edge groups

Details One-ended subgroups of graphs of free groups with cyclic edge groups One-ended subgroups of graphs of free groups with cyclic edge groups

2011-02-14

arxiv.org/abs/1102.2866v2

Mathematics

Group Theory

22 pages, 3 figures, corrected typos in the introduction

Scientific paper

Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of infinite index. As a corollary, the same holds for limit groups. We also obtain a characterisation of surfaces with boundary among free groups equipped with peripheral structures.

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