3 papers
math.GR2025
In Search of Homology for Quasigroups of Bol-Moufang Type
Anthony Christiana, Ben Clingenpeel, Huizheng Guo +3
We initiate (co)homology theory for quasigroups of Bol-Moufang type based on analysis of their extensions by affine quasigroups of the same type. We use these extensions to define…
math.GT2025
Colorings of symmetric unions and partial knots
Ben Clingenpeel, Zongzheng Dai, Gabriel Diraviam +12
Motivated by work of Kinoshita and Teraska, Lamm introduced the notion of a symmetric union, which can be constructed from a partial knot by introducing additional crossings to…
math.GT2025
Low Dimensional Homology of the Yang-Baxter Operators Yielding the HOMFLYPT Polynomial
Anthony Christiana, Ben Clingenpeel, Huizheng Guo +4
In this paper, we analyze the homology of the Yang-Baxter Operators yielding the HOMFLYPT polynomial, reducing the computation of the -th homology of for arb…