Volume and homology of one-cusped hyperbolic 3-manifolds

Abstract

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.

31 pages. This version agrees with the published version of the paper, except that an error in the published abstract has been corrected. In particular, the result which applies to manifolds with mod 2 homology of dimension at least 7 is stronger and has a shorter proof than the corresponding result in version 2