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HEEGAARD GRADIENT OF SEIFERT FIBERED 3-MANIFOLDS

Published online by Cambridge University Press:  14 June 2004

KAZUHIRO ICHIHARA
KAZUHIRO ICHIHARA
Affiliation:
Department of Information and Computer Sciences, Nara Women's University, Kita-Uoya Nishimachi, Nara 630-8506, [email protected]
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Abstract

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.

Keywords

57M10 (primary)57N1057M50 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 36 , Issue 4 , July 2004 , pp. 537 - 546
Copyright
© The London Mathematical Society 2004

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