Horizontal Heegaard Splittings of Seifert Fibered Spaces
نویسنده
چکیده
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 Z. 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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