Algebraic & Geometric Topology 6 (2006) 351–372

DOI: 10.2140/agt.2006.6.351

arXiv: math.GT/0504605

Abstract

We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3–manifolds. Combining this invariant with a theorem of R Weidmann, proved here in the appendix, we show that a closed, totally orientable Seifert fibered space M has infinitely many isotopy classes of Heegaard splittings of the same genus if and only if M has an irreducible, horizontal Heegaard splitting, has a base orbifold of positive genus, and is not a circle bundle. This characterizes precisely which Seifert fibered spaces satisfy the converse of Waldhausen’s conjecture.

Keywords

Heegaard Splitting, essential Surface

Mathematical Subject Classification

Primary: 57M27

Secondary: 57M60, 57N10

References

Publication

Received: 2 May 2005
Revised: 6 December 2005
Accepted: 6
Published: 12 March 2006

Authors