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Surface subgroups from homology

Calegari, Danny (2008) Surface subgroups from homology. Geometry and Topology, 12 (4). pp. 1995-2007. ISSN 1465-3060. doi:10.2140/gt.2008.12.1995.

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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.

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Additional Information:© Copyright 2008 Mathematical Sciences Publishers. Received: 4 April 2008. Revised: 9 June 2008. Accepted: 8 June 2008. Published: 5 July 2008. Proposed: Benson Farb. Seconded: Joan Birman, Dave Gabai. While writing this paper I was partially supported by NSF grant DMS 0707130. I would like to thank Mladen Bestvina, Benson Farb, Lars Louder and Dongping Zhuang for comments and some discussion. I am also very grateful to the anonymous referee for some quick and helpful corrections. The work in this paper builds largely on work done in [4] which benefited greatly from many discussions with Jason Manning.
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National Science FoundationDMS 0707130
Subject Keywords:hyperbolic group, surface subgroup, graph of groups, Thurston norm, rational polyhedron
Issue or Number:4
Record Number:CaltechAUTHORS:CALgt08
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:11509
Deposited By: Archive Administrator
Deposited On:26 Aug 2008 05:25
Last Modified:08 Nov 2021 22:00

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