Volume 16, issue 2 (2012)

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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
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 2010
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/