Geometry & Topology 12 (2008) 1995–2007

DOI: 10.2140/gt.2008.12.1995

Abstract

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

Keywords

hyperbolic group, surface subgroup, graph of groups, Thurston norm, rational polyhedron

Mathematical Subject Classification

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, Dave Gabai

Authors