The Heegaard genus of bundles over S^1
Geometric Topology
2009-03-30 v2
Abstract
This paper explores connections between Heegaard genus, minimal surfaces, and pseudo-Anosov monodromies. Fixing a pseudo-Anosov map phi and an integer n, let M_n be the 3-manifold fibered over S^1 with monodromy phi^n. JH Rubinstein showed that for a large enough n every minimal surface of genus at most h in M_n is homotopic into a fiber; as a consequence Rubinstein concludes that every Heegaard surface of genus at most h for M_n is standard, that is, obtained by tubing together two fibers. We prove this result and also discuss related results of Lackenby and Souto.
Keywords
Cite
@article{arxiv.math/0608517,
title = {The Heegaard genus of bundles over S^1},
author = {Mark Brittenham and Yo'av Rieck},
journal= {arXiv preprint arXiv:math/0608517},
year = {2009}
}
Comments
This is the version published by Geometry & Topology Monographs on 3 December 2007