2008/02/06 by Jesse Johnson, Johnson, Jesse
Mathematics · #57N10 #Advanced Algebra and Geometry #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57N10
paper · pdf · doi:10.48550/arxiv.0802.0856
15 pages, 1 figure
arxiv created 2008/02/06 · openalex publication_date 2008/02/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Z2g. 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.