Volume 6, issue 1 (2006)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 17
Issue 6, 3213–3852
Issue 5, 2565–3212
Issue 4, 1917–2564
Issue 3, 1283–1916
Issue 2, 645–1281
Issue 1, 1–643

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

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

David Bachman and Ryan Derby-Talbot

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
References
Forward citations
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