Horizontal Heegaard splittings of Seifert fibered spaces

Details Horizontal Heegaard splittings of Seifert fibered spaces Horizontal Heegaard splittings of Seifert fibered spaces

2008-02-06

arxiv.org/abs/0802.0856v1

Mathematics

Geometric Topology

15 pages, 1 figure

Scientific paper

We show that if an orientable Seifert fibered space $M$ with an orientable genus $g$ base space admits a strongly irreducible horizontal Heegaard splitting then there is a one-to-one correspondence between isotopy classes of strongly irreducible horizontal Heegaard splittings and elements of $\mathbf{Z}^{2g}$. The correspondence is determined by the slopes of intersection of each Heegaard splitting with a collection of $2g$ incompressible tori in $M$. We also show that there are Seifert fibered spaces with infinitely many non-isotopic Heegaard splittings that determine Nielsen equivalent generating systems for the fundamental group of $M$.

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