176 citations · 1.3k across the 156 of their papers we have counts for
6 papers · 1 filter
Octonions
Jonathan Hackett, Louis H. Kauffman
In this paper we review the topological model for the quaternions based upon the Dirac string trick. We then extend this model, to create a model for the octonions - the non-associ…
Unknotting Unknots
Allison Henrich, Louis H. Kauffman
A knot is an an embedding of a circle into three-dimensional space. We say that a knot is unknotted if there is an ambient isotopy of the embedding to a standard circle. By represe…
A note on amphicheiral alternating links
Louis H. Kauffman, Slavik V. Jablan
After reconsidering the Dasbach-Hougardy counterexample to the Kauffman Conjecture on alternating knots, we reformulate the conjecture and consider Dasbach-Hougardy counterexample…
Oriented Quantum Algebras and Coalgebras, Invariants of Oriented 1-1 Tangles, Knots and Links
Louis Kauffman, David E. Radford
In this paper we study oriented quantum coalgebras which are structures closely related to oriented quantum algebras. We study the relationship between oriented quantum coalgebras…
Quantum Algorithms for the Jones Polynomial
Louis H. Kauffman, Samuel J. Lomonaco
This paper gives a generalization of the AJL algorithm and unitary braid group representation for quantum computation of the Jones polynomial to continuous ranges of values on the…
Topological Quantum Information, Khovanov Homology and the Jones Polynomial
Louis H. Kauffman
In this paper we give a quantum statistical interpretation for the bracket polynomial state sum <K> and for the Jones polynomial. We use this quantum mechanical interpretation to g…