176 citations · 1.3k across the 156 of their papers we have counts for
12 papers · 1 filter
Alexander-Conway Polynomial State Model and Link Homology
Louis H. Kauffman, Marithania Silvero
This paper shows how the Formal Knot Theory state model for the Alexander-Conway polynomial is related to Knot Floer Homology. In particular we prove a parity result about the stat…
Unsolved Problems in Virtual Knot Theory and Combinatorial Knot Theory
Roger Fenn, Denis P. Ilyutko, Louis H. Kauffman +1
This paper is a concise introduction to virtual knot theory, coupled with a list of research problems in this field.
Khovanov Homology, Lee Homology and a Rasmussen Invariant for Virtual Knots
Heather A. Dye, Aaron Kaestner, Louis H. Kauffman
The paper contains an essentially self-contained treatment of Khovanov homology, Khovanov-Lee homology as well as the Rasmussen invariant for virtual knots and virtual knot cobordi…
Virtual Knot Cobordism
Louis H. Kauffman
This paper defines a theory of cobordism for virtual knots and studies this theory for standard and rotational virtual knots and links. Non-trivial examples of virtual slice knots…
A Combinatorial Algorithm for Computing Higher Order Linking Numbers
Chun-Chung Hsieh, Louis Kauffman, Chichen M. Tsau
We develop the intersection theory at relative chain-cochain level, and apply it along with the use of Seifert disks for an oriented link to give a combinatorial algorithm to compu…
Graphical Constructions for the sl(3), so(3) and G2 Invariants for Virtual Knots, Virtual Braids and Free Knots
Louis Hirsch Kauffman, Vassily Olegovich Manturov
We construct graph-valued analogues of the Kuperberg sl(3) and G2 invariants for virtual knots. The restriction of the sl(3) or G2 invariants for classical knots coincides with the…