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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060

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

Henry Wilton

Geometry & Topology 16 (2012) 665–683

DOI: 10.2140/gt.2012.16.665

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.

Keywords

free group, hyperbolic group, surface subgroup

Mathematical Subject Classification

Primary: 20F65, 20F67, 57M07

References
Publication

Received: 28 February 2011
Revised: 1 March 2011
Accepted: 6 January 2012
Published: 24 April 2012
Proposed: Danny Calegari
Seconded: Martin R Bridson, Cameron Gordon

Authors
Henry Wilton
Department of Mathematics
University College London
Gower Street
London
WC1E 6BT
UK
http://www.homepages.ucl.ac.uk/~ucahhjr/