Volume 6 (2006)

Download this article
For screen
For printing
Recent Issues
Volume 1, 2001
Volume 2, 2002
Volume 3, 2003
Volume 4, 2004
Volume 5, 2005
Volume 6, 2006
Volume 7, 2007
Volume 8(1) 2008
Volume 8(2) 2008
Volume 8(3) 2008
Volume 8(4) 2008
Volume 9(1) 2009
Volume 9(2) 2009
Volume 9(3) 2009
Volume 9(4) 2009
Volume 10(1) 2010
The Journal
About the Journal
Editorial Board
Editorial Interests
Author Index
Editorial procedure
Submission Guidelines
Submission Page
Author copyright form
Subscriptions
Contacts
G&T Publications
GTP Author Index

Non-isotopic Heegaard splittings of Seifert fibered spaces

David Bachman and Ryan Derby-Talbot

Appendix: Richard Weidmann

Algebraic & Geometric Topology 6 (2006) 351–372

DOI: 10.2140/agt.2006.6.351

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

Primary: 57M27

Secondary: 57M60, 57N10

References
Publication

Received: 2 May 2005
Revised: 6 December 2005
Accepted: 6
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
Richard Weidmann
Fachbereich Informatik und Mathematik
Johann Wolfgang Goethe-Universität
60054 Frankfurt
Germany