Level-rank duality of knot and link invariants

Howard J. Schnitzer

Level-rank duality of knot and link invariants

Geometric Topology 2021-10-19 v3 High Energy Physics - Theory Mathematical Physics math.MP

Authors: Howard J. Schnitzer

Abstract

A number of results for the level-rank duality of $G(N)_K$ $\leftrightarrow$ $G(K)_N$ Chern-Simons theory are summarized, with emphasis on the applications to knot and link invariants. Explicit examples for $SU(2)_K$ $\leftrightarrow$ $SU(K)_2$ illustrate general results. A criterion to distinguish torus knots and links from hyperbolic knots and links, based on tables constructed by Kaul for one and two strand invariants, is presented. Possible symmetries of hyperbolic knot and link invariants are discussed. The level-rank duality of torus knot and link invariants of minimal models is examined

Keywords

level-rank duality knot invariants link invariants chern-simons theory torus knots hyperbolic knots

Cite

@article{arxiv.2106.15012,
  title  = {Level-rank duality of knot and link invariants},
  author = {Howard J. Schnitzer},
  journal= {arXiv preprint arXiv:2106.15012},
  year   = {2021}
}

Comments

v3: added section on invariants for level -rank dual of minimal models and additional references

Level-rank duality of knot and link invariants

Abstract

Keywords

Cite

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