2002/11/06 by Kazuhiro Ichihara, Ichihara, Kazuhiro
Mathematics · #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #math.GT #msc:57M10 #msc:57M50 #msc:57N10
paper · pdf · doi:10.48550/arxiv.math/0211102
9 pages; revised version; Comments about Heegaard splittings of Seifert fibered 3-manifolds added, proofs in Section 5 revised, and typos corrected
arxiv created 2003/10/27 · arxiv updated 2009/11/30
The infimal Heegaard gradient of a compact 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3-manifolds, and show that a Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it virtually fibers over the circle or over a surface other than the 2-sphere. For a collection of finite coverings of a Seifert fibered 3-manifold, a necessary and sufficient condition to have zero infimal Heegaard gradient is also given.