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Tribracket Modules

Deanna Needell

Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095, USA

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Ave., Claremont, CA 91711, USA

E-mail Address: deanna@math.ucla.edu

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Sam Nelson

http://orcid.org/0000-0003-4973-2467

Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095, USA

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Ave., Claremont, CA 91711, USA

E-mail Address: sam.nelson@cmc.edu

Corresponding author.

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, and

Yingqi Shi

Department of Mathematics, University of California, Los Angeles, 520 Portola Plaza, Los Angeles, CA 90095, USA

Department of Mathematical Sciences, Claremont McKenna College, 850 Columbia Ave., Claremont, CA 91711, USA

E-mail Address: yshi20@students.claremontmckenna.edu

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https://doi.org/10.1142/S0129167X20500287Cited by:2 (Source: Crossref)

Abstract

Niebrzydowski tribrackets are ternary operations on sets satisfying conditions obtained from the oriented Reidemeister moves such that the set of tribracket colorings of an oriented knot or link diagram is an invariant of oriented knots and links. We introduce tribracket modules analogous to quandle/biquandle/rack modules and use these structures to enhance the tribracket counting invariant. We provide examples to illustrate the computation of the invariant and show that the enhancement is proper.

Keywords:

AMSC: 57K10, 57K12

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