Volume 12, issue 4 (2008)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Surface subgroups from homology

Danny Calegari

Geometry & Topology 12 (2008) 1995–2007
Abstract

Let G be a word-hyperbolic group, obtained as a graph of free groups amalgamated along cyclic subgroups. If H2(G; ) is nonzero, then G contains a closed hyperbolic surface subgroup. Moreover, the unit ball of the Gromov–Thurston norm on H2(G; ) is a finite-sided rational polyhedron.

Keywords
hyperbolic group, surface subgroup, graph of groups, Thurston norm, rational polyhedron
Mathematical Subject Classification 2000
Primary: 20F65, 20F67
Secondary: 57M07
References
Publication
Received: 4 April 2008
Revised: 9 June 2008
Accepted: 8 June 2008
Published: 5 July 2008
Proposed: Benson Farb
Seconded: Joan Birman and Dave Gabai
Authors
Danny Calegari
Department of Mathematics
Caltech
Pasadena CA, 91125