Quantizing Knots and Beyond

Abstract

This paper formulates a generalization of our work on quantum knots to explain how to make quantum versions of algebraic, combinatorial and topological structures. We include a description of previous work 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 mathematical structures.

16 pages, 5 figures, LaTeX document

References in corpus (6)

• Non-Abelian Anyons and Topological Quantum Computation
• The BQP-hardness of approximating the Jones Polynomial
• Quantum Knots
• NMR Quantum Calculations of the Jones Polynomial
• A 3-Stranded Quantum Algorithm for the Jones Polynomial
• Quantizing Braids and Other Mathematical Objects: The General Quantization Procedure

Cited by in corpus (4)

• Mosaic number of knots
• Upper bound on the total number of knot $n$-mosaics
• Quantum knots and the number of knot mosaics
• Small knot mosaics and partition matrices