Work

Set-theoretic Yang–Baxter cohomology of cyclic biquandles

Year: 2025

Type: article

Abstract: We completely determine the free parts of the set-theoretic Yang–Baxter (co)homology groups of finite cyclic biquandles, along with fully computing the torsion subgroups of their 1st and 2nd homology groups. Furthermore, we provide upper bounds for the orders of torsions in the 3rd and higher-dimensional homology groups. This work partially solves the conjecture that the normalized set-theoretic Yang–Baxter homology of cyclic biquandles satisfy [Formula: see text] when [Formula: see text] is odd and [Formula: see text] when [Formula: see text] is even. In addition, we obtain cocycle representatives of a basis for the rational cohomology group of a cyclic biquandle and introduce several non-trivial torsion homology classes.

Source: Journal of Knot Theory and Its Ramifications

DOI: 10.1142/s0218216525500129

Authors: Minyi Liang, Xiao Wang, Seung Yeop Yang

Institutions: Jilin University, Kyungpook National University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Research Foundation, National Natural Science Foundation of China, National Research Foundation of Korea, Ministry of Science and ICT, South Korea