Quantizing knots, groups and graphs

Louis H. Kauffman; Samuel J. Lomonaco Jr.

doi:10.1117/12.882567

3 June 2011 Quantizing knots, groups and graphs

Louis H. Kauffman, Samuel J. Lomonaco Jr.

Proceedings Volume 8057, Quantum Information and Computation IX; 80570T (2011) https://doi.org/10.1117/12.882567
Event: SPIE Defense, Security, and Sensing, 2011, Orlando, Florida, United States

Abstract

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.

Citation Download Citation

Louis H. Kauffman and Samuel J. Lomonaco Jr. "Quantizing knots, groups and graphs", Proc. SPIE 8057, Quantum Information and Computation IX, 80570T (3 June 2011); https://doi.org/10.1117/12.882567

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