Homology Theory for the Set-Theoretic Yang-Baxter Equation and Knot Invariants from Generalizations of Quandles

Abstract

A homology theory is developed for set-theoretic Yang-Baxter equations, and knot invariants are constructed by generalized colorings by biquandles and Yang-Baxter cocycles.

Substantially rewritten version which includes computations of Yang Baxter cocycles and evaluations on classical an virtual knots