Geometry & Topology

Surface subgroups from homology

Danny Calegari

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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.

Article information

Source
Geom. Topol., Volume 12, Number 4 (2008), 1995-2007.

Dates
Received: 4 April 2008
Revised: 9 June 2008
Accepted: 8 June 2008
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.gt/1513800119

Digital Object Identifier
doi:10.2140/gt.2008.12.1995

Mathematical Reviews number (MathSciNet)
MR2431013

Zentralblatt MATH identifier
1185.20046

Subjects
Primary: 20F65: Geometric group theory [See also 05C25, 20E08, 57Mxx] 20F67: Hyperbolic groups and nonpositively curved groups
Secondary: 57M07: Topological methods in group theory

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

Citation

Calegari, Danny. Surface subgroups from homology. Geom. Topol. 12 (2008), no. 4, 1995--2007. doi:10.2140/gt.2008.12.1995. https://projecteuclid.org/euclid.gt/1513800119


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