18 citations · 40 across the 14 of their papers we have counts for
15 papers · 1 filter
Virtual Braids and the L--Move
Louis H. Kauffman, Sofia Lambropoulou
In this paper we prove a Markov Theorem for virtual braids and for some analogs of this structure. The virtual braid group is the natural companion in the category of virtual knots…
Virtual Knots and Links
Louis Kauffman, Vassily Olegovich Manturov
This paper is an introduction to the subject of virtual knot theory, combined with a discussion of some specific new theorems about virtual knots. The new results are as follows: W…
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…
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…