HEEGAARD GRADIENT OF SEIFERT FIBERED 3-MANIFOLDS

The infimal Heegaard gradient of a 3-manifold was defined and studied by Marc Lackenby in an approach towards proving the well-known virtually Haken conjecture. As instructive examples, Seifert fibered 3-manifolds are considered in this paper. The author shows that a compact orientable Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if it virtually fibers over either the circle or a surface other than the 2-sphere or, equivalently, if it has infinite fundamental group. 2000 Mathematics Subject Classification 57M10 (primary), 57N10, 57M50 (secondary).