Bikei Module Invariants of Unoriented Surface-Links

Yewon Joung; Sam Nelson

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arXiv · 2204.02520

Bikei Module Invariants of Unoriented Surface-Links

Yewon Joung·Sam Nelson

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Abstract

We extend our previous work from arXiv:1903.06863 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.

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Yewon Joung, Sam Nelson. 2022-04-05. Bikei Module Invariants of Unoriented Surface-Links. https://arxiv.org/abs/2204.02520

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