Jones Polynomial is an invariant of an oriented knot or link which assigns to each oriented knot or link a Laurent polynomial in the variable t^{1/2} with integer coefficients. Though can be computed easily in terms of what are called skein relations, it originally arose from a studying a particular kind of a ‘trace’ of braid representations into an algebra derived as the quotient of a group ring of braid group. We shall discuss this construction of Jones Polynomial in the first talk. In the second part, we shall discuss the construction of Jones Polynomial from the tangle representation of Knots.

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