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Proceedings of the American Mathematical Society

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Biquandle module invariants of oriented surface-links


Authors: 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
Published electronically: April 14, 2020
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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.


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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
Email: yjoung@msu.edu

Sam Nelson
Affiliation: Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Avenue, Claremont, California 91711
Email: sam.nelson@cmc.edu

DOI: https://doi.org/10.1090/proc/14826
Keywords: Biquandle modules, counting invariants, surface-links, marked graph diagrams
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
Article copyright: © Copyright 2020 Yewon Joung and Sam Nelson