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2006 Dehn surgery, homology and hyperbolic volume
Ian Agol, Marc Culler, Peter B Shalen
Algebr. Geom. Topol. 6(5): 2297-2312 (2006). DOI: 10.2140/agt.2006.6.2297

Abstract

If a closed, orientable hyperbolic 3–manifold M has volume at most 1.22 then H1(M;p) has dimension at most 2 for every prime p2,7, and H1(M;2) and H1(M;7) have dimension at most 3. The proof combines several deep results about hyperbolic 3–manifolds. The strategy is to compare the volume of a tube about a shortest closed geodesic CM with the volumes of tubes about short closed geodesics in a sequence of hyperbolic manifolds obtained from M by Dehn surgeries on C.

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Ian Agol. Marc Culler. Peter B Shalen. "Dehn surgery, homology and hyperbolic volume." Algebr. Geom. Topol. 6 (5) 2297 - 2312, 2006. https://doi.org/10.2140/agt.2006.6.2297

Information

Received: 14 July 2006; Accepted: 1 November 2006; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1129.57019
MathSciNet: MR2286027
Digital Object Identifier: 10.2140/agt.2006.6.2297

Subjects:
Primary: 57M50
Secondary: 57M27

Rights: Copyright © 2006 Mathematical Sciences Publishers

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