Volume and homology of one-cusped hyperbolic 3-manifolds

Details Volume and homology of one-cusped hyperbolic 3-manifolds Volume and homology of one-cusped hyperbolic 3-manifolds

2007-07-29

arxiv.org/abs/0707.4300v3

Algebr. Geom. Topol., 8:343--379, 2008

Mathematics

Geometric Topology

31 pages. This version agrees with the published version of the paper, except that an error in the published abstract has been

Scientific paper

10.2140/agt.2008.8.343

Let M be a complete, finite-volume, orientable hyperbolic manifold having exactly one cusp. If we assume that pi_1(M) has no subgroup isomorphic to a genus-2 surface group, and that either (a) H_1(M;Z_p) has dimension at least 5 for some prime p, or (b) H_1(M;Z_2) has dimension at least 4, and the subspace of H^2(M;Z_2) spanned by the image of the cup product has dimension at most 1, then vol M > 5.06 If we assume that H_1(M;Z_2) has dimension at least 7, and that the compact core of M does not contain a genus-2 closed incompressible surface, then vol M > 5.06.

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