Non-isotopic Heegaard splittings of Seifert fibered spaces

Details Non-isotopic Heegaard splittings of Seifert fibered spaces Non-isotopic Heegaard splittings of Seifert fibered spaces

2005-04-29

arxiv.org/abs/math/0504605v4

Algebr. Geom. Topol. 6 (2006) 351-372

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 12 March 2006

Scientific paper

10.2140/agt.2006.6.351

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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