Reformulated invariants for non-torus knots and links
Zodinmawia, P. Ramadevi
TL;DR
This paper computes explicit Chern-Simons invariants for various non-torus knots and links using Racah coefficients, confirming conjectures by Ooguri-Vafa and Labastida-Marino-Vafa through tabulated reformulated invariants.
Contribution
It provides explicit formulas for non-torus knot and link invariants using Racah coefficients, extending previous work and validating key conjectures.
Findings
Reformulated invariants agree with Ooguri-Vafa conjecture for knots.
Reformulated invariants agree with Labastida-Marino-Vafa conjecture for links.
Tabulated invariants facilitate further research in knot theory and quantum topology.
Abstract
Using the Racah coefficients in our earlier paper arXiv:1107.3918, we explicitly write the Chern-Simons field theory invariants for many non-torus knot and links. Further, we have tabulated the reformulated invariants which agrees with the Ooguri-Vafa conjecture for knots and Labastida-Marino-Vafa conjecture for links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Operator Algebra Research