Bikei, Involutory Biracks and Unoriented Link Invariants

Abstract

We identify a subcategory of biracks which define counting invariants of unoriented links, which we call involutory biracks. In particular, involutory biracks of birack rank $N=1$ are biquandles, which we call bikei. We define counting invariants of unoriented classical and virtual links using finite involutory biracks, and we give an example of a non-involutory birack whose counting invariant detects the non-invertibility of a virtual knot.

Type
Publication
Journal of Knot Theory and Its Ramifications