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

Wilton, Henry

doi:10.2140/gt.2012.16.665

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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 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/

Volume 16, issue 2 (2012)