9 citations · 29 across the 7 of their papers we have counts for
20 papers
Set Theoretic Yang-Baxter Solutions via Fox Calculus
J. Scott Carter, Masahico Saito
We construct solutions to the set-theoretic Yang-Baxter equation using braid group representations in free group automorphisms and their Fox differentials. The method resembles the…
A lower bound for the number of Reidemeister moves of type III
J. Scott Carter, Mohamed Elhamdadi, Masahico Saito +1
We study the number of Reidemeister type III moves using Fox n-colorings of knot diagrams.
Problems on invariants of knots and 3-manifolds
J. E. Andersen, N. Askitas, D. Bar-Natan +57
This is a list of open problems on invariants of knots and 3-manifolds with expositions of their history, background, significance, or importance. This list was made by editing ope…
Generalizations of Quandle Cocycle Invariants and Alexander Modules from Quandle Modules
J. Scott Carter, Masahico Saito
This paper is a brief overview of some of our recent results in collaboration with other authors. The cocycle invariants of classical knots and knotted surfaces are summarized, and…
Ribbon concordance of surface-knots via quandle cocycle invariants
J. Scott Carter, Masahico Saito, Shin Satoh
We give necessary conditions of a surface-knot to be ribbon concordant to another, by introducing a new variant of the cocycle invariant of surface-knots in addition to using the i…
Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology
J. Scott Carter, Mohamed Elhamdadi, Matias Graña +1
Three new knot invariants are defined using cocycles of the generalized quandle homology theory that was proposed by Andruskiewitsch and Graña. We specialize that theory to the cas…