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Proceedings of the American Mathematical Society

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

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Biquandle module invariants of oriented surface-links
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by Yewon Joung and Sam Nelson PDF
Proc. Amer. Math. Soc. 148 (2020), 3135-3148

Abstract:

We define invariants of oriented surface-links by enhancing the biquandle counting invariant using biquandle modules, algebraic structures defined in terms of biquandle actions on commutative rings analogous to Alexander biquandles. We show that bead colorings of marked graph diagrams are preserved by Yoshikawa moves and hence define enhancements of the biquandle counting invariant for surface links. We provide examples illustrating the computation of the invariant and demonstrate that these invariants are not determined by the first and second Alexander elementary ideals and characteristic polynomials.
References
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Additional Information
  • Yewon Joung
  • Affiliation: Department of Mathematics, Michigan State University, C120 Wells Hall, 619 Red Cedar Road, East Lansing, Michigan 48824
  • MR Author ID: 1036912
  • Email: yjoung@msu.edu
  • Sam Nelson
  • Affiliation: Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Avenue, Claremont, California 91711
  • MR Author ID: 680349
  • Email: sam.nelson@cmc.edu
  • Received by editor(s): March 16, 2019
  • Received by editor(s) in revised form: August 4, 2019
  • Published electronically: April 14, 2020
  • Additional Notes: The second author was partially supported by Simons Foundation collaboration grant 316709
  • Communicated by: David Futer
  • © Copyright 2020 Yewon Joung and Sam Nelson
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 3135-3148
  • MSC (2010): Primary 57M27, 57M25
  • DOI: https://doi.org/10.1090/proc/14826
  • MathSciNet review: 4099799