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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Links with non-trivial Alexander polynomial which are topologically concordant to the Hopf link
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by Min Hoon Kim, David Krcatovich and JungHwan Park PDF
Trans. Amer. Math. Soc. 371 (2019), 5379-5400 Request permission

Abstract:

We give infinitely many 2-component links with unknotted components which are topologically concordant to the Hopf link, but not smoothly concordant to any 2-component link with trivial Alexander polynomial. Our examples are pairwise non-concordant.
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Additional Information
  • Min Hoon Kim
  • Affiliation: School of Mathematics, Korea Institute for Advanced Study, Seoul 02455, Republic of Korea
  • MR Author ID: 1067137
  • Email: kminhoon@kias.re.kr
  • David Krcatovich
  • Affiliation: Department of Mathematics, Rice University, 6100 Main Street, Houston, Texas 77005
  • MR Author ID: 1128670
  • Email: dk27@rice.edu
  • JungHwan Park
  • Affiliation: Department of Mathematics, Rice University, 6100 Main Street, Houston, Texas 77005
  • MR Author ID: 1188099
  • Email: jp35@rice.edu
  • Received by editor(s): April 5, 2017
  • Received by editor(s) in revised form: August 17, 2017, and September 6, 2017
  • Published electronically: January 15, 2019
  • Additional Notes: The first author was partially supported by the Overseas Research Program for Young Scientists through the Korea Institute for Advanced Study.
    The third author was partially supported by the National Science Foundation grant DMS-1309081.
    The first and the third authors thank the Hausdorff Institute for Mathematics in Bonn for both support and its outstanding research environment.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 371 (2019), 5379-5400
  • MSC (2010): Primary 20J05, 57M07; Secondary 55P60, 57M27
  • DOI: https://doi.org/10.1090/tran/7389
  • MathSciNet review: 3937296