Torus Knots in Adjoint Representation
Andrei Mironov, Vivek Kumar Singh
TL;DR
This paper derives explicit formulas for the adjoint polynomials of torus knots, revealing their structure and significance in the context of Chern-Simons theory and Vogel's universality.
Contribution
It provides a closed-form expression for adjoint polynomials of torus knots, enhancing understanding of their invariants and connections to universal quantum invariants.
Findings
Explicit double sum formula for adjoint polynomials
Deeper insight into the structure of adjoint invariants
Relevance to Vogel's universality in Chern-Simons theory
Abstract
We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of adjoint invariants essential for the Vogel's universality of Chern-Simons theory.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models