Please consider the following links with four components My question is if such two links are isomorphic. The corresponding Jones polynomials are respectively It is observed that the ratio of the Jones polynomials is $q^{9⁄2}$. It is to say the only difference between the two Jones polynomials is a simple monomial. According with such fact […]

Could someone give an laymans explanation of the relation between QFT and knot theory? What are the central ideas in Wittens work on the Jones polynomial?

It is intuitive that one can simply doing a cut-gluing surgery to make a $6^3_2$ to a $3_1$ trefoil knot: e.g. from to All one needs to do it to cut the three intersections at the angle of $\pi/6$, $\pi/6+2\pi/3$, $\pi/6+4\pi/3$ and then gluing three intersections. question: So what is the precise mathematical formulation of […]

Is there a simple formula for a tight approximation of the torus knot length ? (specifically a formula that does not involve integrals or any iterative procedures). The torus knot parameters are $(p, q, R, r)$ where $(p,q)$ are co-primes and $R$ is major axis and $r$ is minor axis of the torus. Note: The […]

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