Virtual shadow modules and their link invariants

Jackson Blankstein; Susan Kim; Catherine Lepel; Sam Nelson; Nicole Sanderson

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arXiv · 1110.1778

Virtual shadow modules and their link invariants

Jackson Blankstein·Susan Kim·Catherine Lepel·Sam Nelson·Nicole Sanderson

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Abstract

We introduce an algebra Z[X,S] associated to a pair (X,S) of a virtual birack X and X-shadow S. We use modules over Z[X,S] to define enhancements of the virtual birack shadow counting invariant, extending the birack shadow module invariants to virtual case. We repeat this construction for the twisted virtual case. As applications, we show that the new invariants can detect orientation reversal and are not determined by the knot group, the Arrow polynomial and the Miyazawa polynomial, and that the twisted version is not determined by the twisted Jones polynomial.

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Jackson Blankstein, Susan Kim, Catherine Lepel, Sam Nelson, Nicole Sanderson. 2012-04-18. Virtual shadow modules and their link invariants. https://arxiv.org/abs/1110.1778

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