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Non-isotopic Heegaard
splittings of Seifert fibered spaces
David Bachman and Ryan Derby-TalbotAppendix: R Weidmann |
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Algebraic & Geometric Topology 6 (2006) 351–372
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arXiv: math.GT/0504605 |
Abstract |
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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 has infinitely many isotopy classes of Heegaard splittings of the same genus if and only if 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. |
Keywords
Heegaard Splitting, essential Surface
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Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57N10, 57M60
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References |
Forward citations |
Publication
Received: 2 May 2005
Revised: 6 December 2005
Published: 12 March 2006
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Authors |
| David Bachman | |
| Mathematics Department Pitzer College 1050 North Mills Avenue Claremont CA 91711 USA |
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| Ryan Derby-Talbot | |
| Mathematics Department The University of Texas at Austin Austin TX 78712-0257 USA |
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| R Weidmann | |
| Fachbereich Informatik und
Mathematik Johann Wolfgang Goethe-Universität 60054 Frankfurt Germany |
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