Geometry & Topology
- Geom. Topol.
- Volume 16, Number 2 (2012), 665-683.
One-ended subgroups of graphs of free groups with cyclic edge groups
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.
Geom. Topol., Volume 16, Number 2 (2012), 665-683.
Received: 28 February 2011
Revised: 1 March 2011
Accepted: 6 January 2012
First available in Project Euclid: 20 December 2017
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Wilton, Henry. One-ended subgroups of graphs of free groups with cyclic edge groups. Geom. Topol. 16 (2012), no. 2, 665--683. doi:10.2140/gt.2012.16.665. https://projecteuclid.org/euclid.gt/1513732406