Incompressible surfaces, hyperbolic volume, Heegaard genus and homology
Geometric Topology
2009-01-07 v2
Abstract
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.
Keywords
Cite
@article{arxiv.0807.4718,
title = {Incompressible surfaces, hyperbolic volume, Heegaard genus and homology},
author = {Marc Culler and Jason DeBlois and Peter B. Shalen},
journal= {arXiv preprint arXiv:0807.4718},
year = {2009}
}
Comments
24 pages, some typographical errors have been corrected and a few passages were reworded to improve clarity