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

Henry Wilton
2012 Geometry and Topology  
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.
doi:10.2140/gt.2012.16.665 fatcat:f3g3heqqn5hf5fu6tuupvtepjy