Research ArticleNo Access

Bikei module invariants of unoriented surface-links

Yewon Joung

https://orcid.org/0009-0001-5721-1146

Department of Mathematics, Hanyang University, Seoul 04763, Republic of Korea

E-mail Address: yewonjoung@hanyang.ac.kr

Corresponding author.

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and

Sam Nelson

Department of Mathematical Sciences, Claremont McKenna College, Claremont, CA 91711, USA

E-mail Address: Sam.Nelson@cmc.edu

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https://doi.org/10.1142/S0218216523500657Cited by:0 (Source: Crossref)

Abstract

We extend our previous work on biquandle module invariants of oriented surface-links to the case of unoriented surface-links using bikei modules. The resulting infinite family of enhanced invariants proves be effective at distinguishing unoriented and especially non-orientable surface-links; in particular, we show that these invariants are more effective than the bikei homset cardinality invariant alone at distinguishing non-orientable surface-links. Moreover, as another application we note that our previous biquandle modules which do not satisfy the bikei module axioms are capable of distinguishing different choices of orientation for orientable surface-links as well as classical and virtual links.

Keywords:

AMSC: 57K12, 57K45

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