Virtual shadow modules and their link invariants [article]

Jackson Blankstein and Susan Kim and Catherine Lepel and Sam Nelson and Nicole Sanderson
2012 arXiv   pre-print
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
more » ... e twisted version is not determined by the twisted Jones polynomial.
arXiv:1110.1778v2 fatcat:6ubatxdx7veyxpsdldzvhtms24