Virtual shadow modules and their link invariants
Geometric Topology
2012-04-20 v2 Quantum Algebra
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.
Keywords
Cite
@article{arxiv.1110.1778,
title = {Virtual shadow modules and their link invariants},
author = {Jackson Blankstein and Susan Kim and Catherine Lepel and Sam Nelson and Nicole Sanderson},
journal= {arXiv preprint arXiv:1110.1778},
year = {2012}
}
Comments
18 pages. Version 2 includes typo corrections. To appear in Int'l. J. Math