176 citations · 1.3k across the 156 of their papers we have counts for
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On Vassiliev Invariants of Virtual Knots
Wout Moltmaker, Louis H. Kauffman
We discuss Vassiliev invariants for virtual knots, expanding upon the theory of quantum virtual knot invariants developed in arXiv:1509.00578. In particular, following the theory o…
Topology of Vortex Reconnection
Louis H. Kauffman
Knotted vortices such as those produced in water by Kleckner and Irvine tend to transform by reconnection to collections of unknotted and unlinked circles. The reconnection number…
New invariants for virtual knots via spanning surfaces
András Juhász, Louis H. Kauffman, Eiji Ogasa
We define three different types of spanning surfaces for knots in thickened surfaces. We use these to introduce new Seifert matrices, Alexander-type polynomials, genera, and a sign…
Combinatorial Knot Theory and the Jones Polynomial
Louis H Kauffman
This paper is a memory of the work and influence of Vaughan Jones. It is an exposition of the remarkable breakthroughs in knot theory and low dimensional topology that were catalyz…
Quantum Invariants of Links and 3-Manifolds with Boundary defined via Virtual Links: Calculation of some examples
Heather A. Dye, Louis H. Kauffman, Eiji Ogasa
In the prequel of this paper, Kauffman and Ogasa introduced new topological quantum invariants of compact oriented 3-manifolds with boundary where the boundary is a disjoint union…
Knot Dynamics
Louis H Kauffman
We examine computer experiments that can be performed to understand the dynamics of knots under self-repulsion. In the course of specific computer exploration we use the knot theor…