Equivalence of two definitions of set-theoretic Yang-Baxter homology

2016/11/03 by Przytycki, Jozef H., Wang, Xiao · 1 citation
#FOS: Mathematics #Geometric Topology (math.GT) #Primary 57M25 #Secondary 18G60

paper · doi:10.48550/arxiv.1611.01178

Abstract

In 2004, Carter, Elhamdadi and Saito defined a homology theory for set-theoretic Yang-Baxter operators(we will call it the "algebraic" version in this article). In 2012, Przytycki defined another homology theory for pre-Yang-Baxter operators which has a nice graphic visualization(we will call it the "graphic" version in this article). We show that they are equivalent. The "graphic" homology is also defined for pre-Yang-Baxter operators, and we give some examples of it's one-term and two-term homologies. In the two-term case, we have found torsion in homology of Yang-Baxter operator that yields the Jones polynomial.

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