176 citations · 1.3k across the 156 of their papers we have counts for
6 papers · 2 filters
Virtual Biquandles
Louis Kauffman, Vassily Olegovich Manturov
In the present paper, we describe new approaches for constructing virtual knot invariants. The main background of this paper comes from formulating and bringing together the ideas…
Virtual Braids
Louis H. Kauffman, Sofia Lambropoulou
In the present paper we give a new method for converting virtual knots and links to virtual braids. Indeed the braiding method given in this paper is quite general, and applies to…
Virtual Knot Diagrams and the Witten-Reshetikhin-Turaev Invariant
H. A. Dye, Louis H. Kauffman
The Witten-Reshetikhin-Turaev invariant of classical link diagrams is generalized to virtual link diagrams. This invariant is unchanged by the framed Reidemeister moves and the Kir…
A Self-Linking Invariant of Virtual Knots
Louis H. Kauffman
In this paper we introduce a new invariant of virtual knots and links that is non-trivial for infinitely many virtuals, but is trivial on classical knots and links. The invariant i…
Minimal Flat Knotted Ribbons
Louis H. Kauffman
This paper gives mathematical models for flat knotted ribbons, and makes specific conjectures for the least length of ribbon (for a given width) needed to tie the trefoil knot and…
Minimal surface representations of virtual knots and links
H. A. Dye, Louis H. Kauffman
Kuperberg [Algebr. Geom. Topol. 3 (2003) 587-591] has shown that a virtual knot corresponds (up to generalized Reidemeister moves) to a unique embedding in a thichened surface of m…