Non-isotopic Heegaard splittings of Seifert fibered spaces

David Bachman, Ryan Derby-Talbot
2006 Algebraic and Geometric Topology  
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
more » ... This characterizes precisely which Seifert fibered spaces satisfy the converse of Waldhausen's conjecture.
doi:10.2140/agt.2006.6.351 fatcat:tz7w6bys6nfgzg2zkoapnn2zjm