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

Abstract

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.

22 pages, 3 figures, corrected typos in the introduction

References in corpus (3)

• On surface subgroups of doubles of free groups
• Line Patterns in Free Groups
• Polygonal words in free groups

Cited by in corpus (5)

• On the one-endedness of graphs of groups
• Immersed cycles and the JSJ decomposition
• JSJ decompositions of Quadratic Baumslag-Solitar groups
• Graph of groups decompositions of graph braid groups
• Vertex links and the Grushko decomposition