What are the Jones polynomials for the torus links and the closure of the other braid word below?
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I am working on a project to determine the Jones polynomial for the torus links and a class of links which I call tst links. Their braid words are respectively given by $$(sigma_1 sigma_2 cdots sigma_{p-1})^q in B_p$$ and $$(sigma_1^2 sigma_2 sigma_3 cdots sigma_p)^q in B_{p+1}$$ I would like to know if anyone familiar with the Ocneanu approach, Chern-Simons Theory approach, and the Burau representations approach can evaluate the Jones polynomials and give a clear, detailed explanation.
knot-theory low-dimensional-topology knot-invariants
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edited 2 days ago
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