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2008 Volume and homology of one-cusped hyperbolic $3$–manifolds
Marc Culler, Peter B Shalen
Algebr. Geom. Topol. 8(1): 343-379 (2008). DOI: 10.2140/agt.2008.8.343

Abstract

Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that π1(M) has no subgroup isomorphic to a genus–2 surface group and that either (a) dimpH1(M;p)5 for some prime p, or (b) dim2H1(M;2)4, and the subspace of H2(M;2) spanned by the image of the cup product H1(M;2)×H1(M;2)H2(M;2) has dimension at most 1, then volM>5.06. If we assume that dim2H1(M;2)7 and that the compact core N of M contains a genus–2 closed incompressible surface, then volM>5.06. Furthermore, if we assume only that dim2H1(M;2)7, then volM>3.66.

Citation

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Marc Culler. Peter B Shalen. "Volume and homology of one-cusped hyperbolic $3$–manifolds." Algebr. Geom. Topol. 8 (1) 343 - 379, 2008. https://doi.org/10.2140/agt.2008.8.343

Information

Received: 24 August 2007; Revised: 3 February 2007; Accepted: 17 December 2007; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1160.57012
MathSciNet: MR2443232
Digital Object Identifier: 10.2140/agt.2008.8.343

Subjects:
Primary: 57M50
Secondary: 57M27

Rights: Copyright © 2008 Mathematical Sciences Publishers

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