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From Goeritz matrices to quasi-alternating links
Jozef H. Przytycki
Knot Theory is currently a very broad field. Even a long survey can only cover a narrow area. Here we concentrate on the path from Goeritz matrices to quasi-alternating links. On t…
Survey on recent invariants on classical knot theory
Jozef H. Przytycki
The survey we are presenting is over 22 years old but it has still some ideas which where never published (except in Polish). This survey is the base of the third Chapter of my boo…
Signature of rotors
Mieczyslaw K. Dabkowski, Makiko Ishiwata, Jozef H. Przytycki +1
Rotors were introduced in Graph Theory by W.Tutte. The concept was adapted to Knot Theory as a generalization of mutation by Anstee, Przytycki and Rolfsen in 1987. In this paper we…
Knot polynomials and generalized mutation
Richard P. Anstee, Jozef H. Przytycki, Dale Rolfsen
The motivation for this work was to construct a nontrivial knot with trivial Jones polynomial. Although that open problem has not yielded, the methods are useful for other problems…
Khovanov homology: torsion and thickness
Marta M. Asaeda, Jozef H. Przytycki
We partially solve the conjecture by A.Shumakovitch about torsion in the Khovanov homology of prime, non-split links in S^3. We give a size restriction on the Khovanov homology of…