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G&T Monographs |
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Surface subgroups from homology
Danny Calegari
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Geometry & Topology 12 (2008)
1995–2007
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Abstract
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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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Keywords
hyperbolic group, surface subgroup, graph
of groups, Thurston norm, rational polyhedron
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Mathematical Subject Classification
Primary: 20F65, 20F67
Secondary: 57M07
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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
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