Vol. 298, No. 2, 2019

Download this article
Download this article For screen
For printing
Recent Issues
Vol. 306: 1  2
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Online Archive
The Journal
Editorial Board
Special Issues
Submission Guidelines
Submission Form
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
Other MSP Journals
Concordance of Seifert surfaces

Robert Myers

Vol. 298 (2019), No. 2, 429–444

We prove that every oriented nondisk Seifert surface F for an oriented knot  K in S3 is smoothly concordant to a Seifert surface F for a hyperbolic knot K of arbitrarily large volume. This gives a new and simpler proof of the result of Friedl and of Kawauchi that every knot is S-equivalent to a hyperbolic knot of arbitrarily large volume. The construction also gives a new and simpler proof of the result of Silver and Whitten and of Kawauchi that for every knot K there is a hyperbolic knot K of arbitrarily large volume and a map of pairs f : (S3,K) (S3,K) which induces an epimorphism on the knot groups. An example is given which shows that knot Floer homology is not an invariant of Seifert surface concordance. We also prove that a set of finite volume hyperbolic 3-manifolds with unbounded Haken numbers has unbounded volumes.

knot, Seifert surface, concordance
Mathematical Subject Classification 2010
Primary: 57M25
Received: 4 January 2017
Revised: 18 May 2018
Accepted: 6 June 2018
Published: 8 March 2019
Robert Myers
Department of Mathematics
Oklahoma State University
United States