Quantizing knots, groups and graphs
Louis Hirsch Kauffman, Samuel J. Lomonaco · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2011
This paper formulates a generalization of our work on quantum knots to explain how to make quantum versions of algebraic and combinatorial structures. We include a description of work of the first author on the construction of Hilbert spaces from the states of the bracket polynomial with applications to algorithms for the Jones polynomial and relations with Khovanov homology. The purpose of this paper is to place such constructions in a general context of the quantization of combinatorial structures.