6 papers
Path to homology of Yang-Baxter operators
Jozef H. Przytycki
The paper surveys the historical development of knot theory and then traces the author's work on defining homology theories for Yang‑Baxter operators, combining known material with…
Kauffman bracket skein module of the connected sum of two solid tori
Rhea Palak Bakshi, Thang T. Q. Lê, Józef H. Przytycki
We determine the structure of the Kauffman bracket skein module of the connected sum of two genus one handlebodies over the ring of Laurent polynomials , ther…
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…
The Montesinos-Nakanishi 3-move conjecture for links up to 20 crossings
Rhea Palak Bakshi, Benjamin A. Burton, Huizheng Guo +4
Yasutaka Nakanishi formulated the following conjecture in 1981: every link is 3-move equivalent to a trivial link. While the conjecture was proved for several specific cases, it re…
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…