Algebraic & Geometric Topology

Non-isotopic Heegaard splittings of Seifert fibered spaces

David Bachman and Ryan Derby-Talbot

Full-text: Open access

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.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 1 (2006), 351-372.

Dates
Received: 2 May 2005
Revised: 6 December 2005
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796516

Digital Object Identifier
doi:10.2140/agt.2006.6.351

Mathematical Reviews number (MathSciNet)
MR2220681

Zentralblatt MATH identifier
1099.57015

Subjects
Primary: 57M27: Invariants of knots and 3-manifolds
Secondary: 57N10: Topology of general 3-manifolds [See also 57Mxx] 57M60: Group actions in low dimensions

Keywords
Heegaard Splitting essential Surface

Citation

Bachman, David; Derby-Talbot, Ryan. Non-isotopic Heegaard splittings of Seifert fibered spaces. Algebr. Geom. Topol. 6 (2006), no. 1, 351--372. doi:10.2140/agt.2006.6.351. https://projecteuclid.org/euclid.agt/1513796516


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