Geometry & Topology

Surface subgroups from homology

Danny Calegari

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.

Article information

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

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

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

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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