On set-theoretic Yang-Baxter cohomology groups of cyclic biquandles

Abstract

We determine the Betti numbers for the (degenerate and normalized) set-theoretic Yang-Baxter (co)homology groups of cyclic biquandles and estimate their torsion subgroups. This partially settles the conjecture presented in [24]. We also obtain cocycles which are representatives of the elements of a basis for the free part of the cohomology group of a cyclic biquandle.