论文信息 - Non-isotopic Heegaard splittings of Seifert fibered spaces

Non-isotopic Heegaard splittings of Seifert fibered spaces

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. 57M27; 57N10, 57M60

D. Bachman | Ryan Derby-Talbot

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