Non-isotopic Heegaard splittings of Seifert fibered spaces

David Bachman; Ryan Derby-Talbot

doi:10.2140/agt.2006.6.351

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Non-isotopic Heegaard splittings of Seifert fibered spaces

David Bachman·Ryan Derby-Talbot

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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.

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BibTeX RIS

David Bachman, Ryan Derby-Talbot. 2009-03-06. Non-isotopic Heegaard splittings of Seifert fibered spaces. https://doi.org/10.2140/agt.2006.6.351

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