Geometry & Topology Monographs 12 (2007) 17–33

DOI: 10.2140/gtm.2007.12.17

arXiv: math.GT/0608517

Abstract

This paper explores connections between Heegaard genus, minimal surfaces, and pseudo-Anosov monodromies. Fixing a pseudo-Anosov map φ and an integer n, let M_n be the 3–manifold fibered over S¹ with monodromy φⁿ.

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

Heegard genus, pseudo-Anosov monodromy, minimal surface

Mathematical Subject Classification

Primary: 57M50

Secondary: 57M10

References

Publication

Received: 27 July 2006
Revised: 19 April 2007
Accepted: 20 April 2007
Published: 3 December 2007

Authors