Virtual shadow modules and their link invariants

  title={Virtual shadow modules and their link invariants},
  author={Jackson Blankstein and Susan Kim and Catherine Lepel and Sam Nelson and Nicole F. Sanderson},
  journal={arXiv: Geometric Topology},
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… 
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