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Heegaard Gradient of Seifert Fibered 3‐Manifolds
Author(s) -
Ichihara Kazuhiro
Publication year - 2004
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609304003182
Subject(s) - fibered knot , mathematics , 3 manifold , conjecture , manifold (fluid mechanics) , pure mathematics , surface (topology) , heegaard splitting , combinatorics , mathematical analysis , geometry , mechanical engineering , engineering
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).