176 citations · 1.3k across the 156 of their papers we have counts for
9 papers · 2 filters
The Affine Index Polynomial and the Sawollek Polynomial
Louis H Kauffman
The purpose of this paper is to give a new basis for examining the relationships of the Affine Index Polynomial and the Sawollek Polynomial. Blake Mellor has written a pioneering p…
Rectangular knot diagrams classification with deep learning
L. H. Kauffman, N. E. Russkikh, I. A. Taimanov
In this article we discuss applications of neural networks to recognising knots and, in particular, to the unknotting problem. One of motivations for this study is to understand ho…
On ribbon graphs and virtual links
Scott Baldridge, Louis H. Kauffman, William Rushworth
We introduce a new equivalence relation on decorated ribbon graphs, and show that its equivalence classes directly correspond to virtual links. We demonstrate how this corresponden…
Finite type invariants for knotoids
Manousos Manouras, Sofia Lambropoulou, Louis H. Kauffman
We extend the theory of Vassiliev (or finite type) invariants for knots to knotoids using two different approaches. Firstly, we take closures on knotoids to obtain knots and we use…
Khovanov-Lipshitz-Sarkar homotopy type for links in thickened higher genus surfaces
Louis H. Kauffman, Igor Mikhailovich Nikonov, Eiji Ogasa
We discuss links in thickened surfaces. We define the Khovanov-Lipshitz-Sarkar stable homotopy type and the Steenrod square for the homotopical Khovanov homology of links in thicke…
On arrow polynomials of checkerboard colorable virtual links
Qingying Deng, Xian'an Jin, Louis H. Kauffman
In this paper we give two new criteria of detecting the checkerboard colorability of virtual links by using odd writhe and arrow polynomial of virtual links, respectively. By apply…
Knot polynomials of open and closed curves
Eleni Panagiotou, Louis H. Kauffman
In this manuscript we introduce a method to measure entanglement of curves in 3-space that extends the notion of knot and link polynomials to open curves. We define the bracket pol…
Steenrod square for virtual links toward Khovanov-Lipshitz-Sarkar stable homotopy type for virtual links
Louis H. Kauffman, Eiji Ogasa
We define a second Steenrod square for virtual links, which is stronger than Khovanov homology for virtual links, toward constructing Khovanov-Lipshitz-Sarkar stable homotopy type…
Unoriented Virtual Khovanov Homology
Scott Baldridge, Louis H. Kauffman, Ben McCarty
The Jones polynomial and Khovanov homology of a classical link are invariants that depend upon an initial choice of orientation for the link. In this paper, we give a Khovanov homo…