Heegaard gradient of Seifert fibered 3-manifold

Details Heegaard gradient of Seifert fibered 3-manifold Heegaard gradient of Seifert fibered 3-manifold

2002-11-06

arxiv.org/abs/math/0211102v2

Mathematics

Geometric Topology

9 pages; revised version; Comments about Heegaard splittings of Seifert fibered 3-manifolds added, proofs in Section 5 revised

Scientific paper

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.

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