Marc Culler, Jason DeBlois, Peter B. Shalen
Published 2008-07-29, updated 2009-01-07Version 2
We show that if M is a complete, finite-volume, hyperbolic 3-manifold having exactly one cusp, and if H_1(M;Z_2) has dimension at least 6, then M has volume greater than 5.06. We also show that if M is a closed, orientable hyperbolic 3-manifold such that H_1(M;Z_2) has dimension at least 4, and if the image of the cup product map in H^2(M;Z_2) has dimension at most 1, then M has volume greater than 3.08. The proofs of these geometric results involve new topological results relating the Heegaard genus of a closed Haken manifold M to the Euler characteristic of the kishkes (i.e guts) of the complement of an incompressible surface in M.
Comments: 24 pages, some typographical errors have been corrected and a few passages were reworded to improve clarity
Hyperbolic volume, Heegaard genus and ranks of groups
Degree one maps between small 3-manifolds and Heegaard genus
The Heegaard genus of bundles over S^1
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