5 papers
Fundamentals of cubic skein modules
Rhea Palak Bakshi, Anthony Christiana, Huizheng Guo +6
Over the past thirty-seven years, the study of linear and quadratic skein modules has produced a rich and far-reaching skein theory, intricately connected to diverse areas of mathe…
Every -Bundle over a positive genus() Surface has Mapping Class Group of Infinite Rank
Huizheng Guo
In 2025, Lin, Wu, Xie and Zhang extend Dax invariant from embedded disks to embedded surfaces and show that there is surjective homomorphism from to …
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…
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…
Using Fibonacci Numbers and Chebyshev Polynomials to Express Fox Coloring Groups and Alexander-Burau-Fox Modules of Diagrams of Wheel Graphs
Anthony Christiana, Huizheng Guo, Jozef H. Przytycki
In this paper we compute the Reduced Fox Coloring Group of the diagrams of Wheel Graphs which can also be represented at the closure of the braids . In doing so,…