1992/10/01 by F. Y. Wu · 1 voice
Mathematics · #Geometric and Algebraic Topology #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models
paper · doi:10.1103/revmodphys.64.1099
openalex publication_date 1992/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/15
This is a tutorial review on knot invariants and their construction using the method of statistical mechanics. We begin with brief reviews of the elements of knot theory and relevant results in statistical mechanics. We then show how knot invariants, including those discovered recently, can be obtained by applying techniques used in solving lattice models in lattice statistics. Our approach is based on the consideration of solvable models with strictly local Boltzmann weights. The presentation, which is self-contained and elementary, is intended for a general readership. A table of polynomial invariants for knot and links containing up to six crossings is included in the Appendix.