Horizontal Heegaard splittings of Seifert fibered spaces - Mathematics > Geometric Topology

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

Author: Jesse Johnson

Source: https://arxiv.org/