Incompressible surfaces, hyperbolic volume, Heegaard genus and homology

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

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.
24 pages, some typographical errors have been corrected and a few passages were reworded to improve clarity

Keywords

Geometric Topology, 57M50

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/214672

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0807.4718
 http://arxiv.org/abs/0807.4718

Collections

arXiv