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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Average four-genus of two-bridge knots
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by S. Baader, A. Kjuchukova, L. Lewark, F. Misev and A. Ray;
Proc. Amer. Math. Soc. 153 (2025), 357-362
DOI: https://doi.org/10.1090/proc/14784
Published electronically: November 25, 2024

Abstract:

We prove that the expected value of the ratio between the smooth four-genus and the Seifert genus of two-bridge knots tends to zero as the crossing number tends to infinity.
References
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Bibliographic Information
  • S. Baader
  • Affiliation: Mathematisches Institut, Sidlerstr. 5, 3012 Bern, Switzerland
  • MR Author ID: 757518
  • Email: sebastian.baader@math.unibe.ch
  • A. Kjuchukova
  • Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
  • MR Author ID: 1272582
  • Email: sashka@mpim-bonn.mpg.de
  • L. Lewark
  • Affiliation: Mathematisches Institut, Sidlerstr. 5, 3012 Bern, Switzerland
  • MR Author ID: 1064492
  • ORCID: 0000-0002-1569-9219
  • Email: lukas@lewark.de
  • F. Misev
  • Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
  • MR Author ID: 1254979
  • Email: fmisev@mpim-bonn.mpg.de
  • A. Ray
  • Affiliation: Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany
  • MR Author ID: 1039665
  • ORCID: 0000-0002-5620-4139
  • Email: aruray@mpim-bonn.mpg.de
  • Received by editor(s): April 10, 2019
  • Received by editor(s) in revised form: July 3, 2019
  • Published electronically: November 25, 2024
  • Additional Notes: The second author was partially supported by NSF grant DMS-1821257
  • Communicated by: David Futer
  • © Copyright 2024 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 153 (2025), 357-362
  • MSC (2020): Primary 57K10
  • DOI: https://doi.org/10.1090/proc/14784
  • MathSciNet review: 4840282