Dehn surgery, homology and hyperbolic volume

Ian Agol; Marc Culler; Peter B Shalen

doi:10.2140/agt.2006.6.2297

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Dehn surgery, homology and hyperbolic volume

Ian Agol·Marc Culler·Peter B Shalen

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Abstract

If a closed, orientable hyperbolic 3--manifold M has volume at most 1.22 then H_1(M;Z_p) has dimension at most 2 for every prime p not 2 or 7, and H_1(M;Z_2) and H_1(M;Z_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 C in M 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. 2009-07-06. Dehn surgery, homology and hyperbolic volume. https://doi.org/10.2140/agt.2006.6.2297

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