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2006 Non-isotopic Heegaard splittings of Seifert fibered spaces
David Bachman, Ryan Derby-Talbot
Algebr. Geom. Topol. 6(1): 351-372 (2006). DOI: 10.2140/agt.2006.6.351

Abstract

We find a geometric invariant of isotopy classes of strongly irreducible Heegaard splittings of toroidal 3–manifolds. Combining this invariant with a theorem of R Weidmann, proved here in the appendix, we show that a closed, totally orientable Seifert fibered space M has infinitely many isotopy classes of Heegaard splittings of the same genus if and only if M has an irreducible, horizontal Heegaard splitting, has a base orbifold of positive genus, and is not a circle bundle. This characterizes precisely which Seifert fibered spaces satisfy the converse of Waldhausen’s conjecture.

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David Bachman. Ryan Derby-Talbot. "Non-isotopic Heegaard splittings of Seifert fibered spaces." Algebr. Geom. Topol. 6 (1) 351 - 372, 2006. https://doi.org/10.2140/agt.2006.6.351

Information

Received: 2 May 2005; Revised: 6 December 2005; Published: 2006
First available in Project Euclid: 20 December 2017

zbMATH: 1099.57015
MathSciNet: MR2220681
Digital Object Identifier: 10.2140/agt.2006.6.351

Subjects:
Primary: 57M27
Secondary: 57M60, 57N10

Rights: Copyright © 2006 Mathematical Sciences Publishers

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