Geodesic
Non-isotopic Heegaard splittings of Seifert fibered spaces
Bachman, David1 ; Derby-Talbot, Ryan2
1Mathematics Department, Pitzer College, 1050 North Mills Avenue, Claremont CA 91711, USA
2Mathematics Department, The University of Texas at Austin, Austin TX 78712-0257, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 351-372
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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 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.

DOI : 10.2140/agt.2006.6.351
Keywords: Heegaard Splitting, essential Surface

Bachman, David  1   ; Derby-Talbot, Ryan  2

1 Mathematics Department, Pitzer College, 1050 North Mills Avenue, Claremont CA 91711, USA
2 Mathematics Department, The University of Texas at Austin, Austin TX 78712-0257, USA 
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Bachman, David; Derby-Talbot, Ryan. Non-isotopic Heegaard splittings of Seifert fibered spaces. Algebraic and Geometric Topology, Tome 6 (2006) no. 1, pp. 351-372. doi: 10.2140/agt.2006.6.351

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