Low Dimensional Homology of the Yang-Baxter Operators Yielding the HOMFLYPT Polynomial

2025/02/28 by Christiana, Anthony, Clingenpeel, Ben, Guo, Huizheng +4
#16T25 (secondary) #57K10 (primary) #FOS: Mathematics #Geometric Topology (math.GT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2502.20659

Abstract

In this paper, we analyze the homology of the Yang-Baxter Operators R_(m) yielding the HOMFLYPT polynomial, reducing the computation of the n-th homology of R_(m) for arbitrary m to the computation of n+1 initial conditions. We then produce the explicit formulas for the third and fourth homology.

Related

• The second Yang-Baxter homology for the Homflypt polynomial
• Path to homology of Yang-Baxter operators
• Equivalence of two definitions of set-theoretic Yang-Baxter homology
• On the Hilbert Polynomial of the HOMFLYPT Homology
• Homology of Yang-Baxter modules