Horizontal Heegaard splittings of Seifert fibered spaces

Jesse Johnson

Vol. 245 (2010), No. 1, 151–165

DOI: 10.2140/pjm.2010.245.151

Abstract

We show that if an orientable Seifert fibered space M with an orientable genus g base space admits a strongly irreducible horizontal Heegaard splitting, then there is a one-to-one correspondence between isotopy classes of strongly irreducible horizontal Heegaard splittings and elements of ℤ^2g. This correspondence is determined by the slopes of intersection of each Heegaard splitting with a set of 2g incompressible tori in M. We also show there are Seifert fibered spaces with infinitely many nonisotopic Heegaard splittings that determine Nielsen equivalent generating systems for the fundamental group of M.

Keywords

Heegaard splitting, Seifert fibered space, Nielsen equivalence

Mathematical Subject Classification 2000

Primary: 57N10

Milestones

Received: 22 September 2008

Revised: 30 April 2009

Accepted: 12 May 2009

Published: 20 January 2010