Myers, Robert2025-01-152025-01-152019-02Myers, R. (2019). Concordance of Seifert surfaces. Pacific Journal of Mathematics, 298(2), pp. 429-444. https://doi.org/10.2140/pjm.2019.298.4290030-8730https://hdl.handle.net/20.500.14446/345772First published in Pacific Journal of Mathematics in Vol. 298 (2019), No. 2, published by Mathematical Sciences PublishersWe 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.application/pdfThis material has been previously published. In the Oklahoma State University Library's institutional repository this version is made available through the open access principles and the terms of agreement/consent between the author(s) and the publisher. The permission policy on the use, reproduction or distribution of the material falls under fair use for educational, scholarship, and research purposes. Contact Digital Resources and Discovery Services at lib-dls@okstate.edu or 405-744-9161 for further information.10.2140/pjm.2019.298.429Articlepure mathematicsmathematical sciencesgeneral mathematicsknotSeifert surfaceconcordanceORCID: 0009-0008-5271-4140 (Myers, R)ScopusID: 7403700679 (Myers, R)0030-8730