Volume 6, issue 1 (2006)

 Recent Issues
Author Index
 The Journal About the Journal Editorial Board Subscriptions Editorial Interests Editorial Procedure Submission Guidelines Submission Page Ethics Statement ISSN (electronic): 1472-2739 ISSN (print): 1472-2747 To Appear Other MSP Journals
Non-isotopic Heegaard splittings of Seifert fibered spaces

Appendix: R Weidmann

Algebraic & Geometric Topology 6 (2006) 351–372
 arXiv: math.GT/0504605
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.

Keywords
Heegaard Splitting, essential Surface
Mathematical Subject Classification 2000
Primary: 57M27
Secondary: 57N10, 57M60
Publication
Received: 2 May 2005
Revised: 6 December 2005
Published: 12 March 2006
Authors
 David Bachman Mathematics Department Pitzer College 1050 North Mills Avenue Claremont CA 91711 USA Ryan Derby-Talbot Mathematics Department The University of Texas at Austin Austin TX 78712-0257 USA R Weidmann Fachbereich Informatik und Mathematik Johann Wolfgang Goethe-Universität 60054 Frankfurt Germany