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.

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

References in corpus (3)

• Set-theoretical solutions to the quantum Yang-Baxter equation
• On set-theoretical solutions of the quantum Yang-Baxter equation
• On Alexander-Conway Polynomials for Virtual Knots and Links

Cited by in corpus (4)

• Torsion in one-term distributive homology
• Bikei, Involutory Biracks and unoriented link invariants
• Virtual Yang-Baxter cocycle invariants
• The column group and its link invariants