A recursive formula for the Jones polynomial of 2-bridge links and applications
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In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C(-2n_1,2n_2,-2n_3,…, (-1)^r2n_r) in terms of n_1, n_2,…, n_r. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link L^(3) with rational quotient L = C(2, n_1, -2, n_2,…,n_r, (-1)^r 2) for any nonzero integers n_1, n_2,…,n_r and give a formula for the span of the Jones polynomial of L^(3) in terms of n_1, n_2,…, n_r with n_i ≠ ±1 for all i = 1, 2,…,r.
Abstract
In this paper, we give a recursive formula for the Jones polynomial of a 2-bridge knot or link with Conway normal form C(-2n_1,2n_2,-2n_3,…, (-1)^r2n_r) in terms of n_1, n_2,…, n_r. As applications, we also give a recursive formula for the Jones polynomial of a 3-periodic link L^(3) with rational quotient L = C(2, n_1, -2, n_2,…,n_r, (-1)^r 2) for any nonzero integers n_1, n_2,…,n_r and give a formula for the span of the Jones polynomial of L^(3) in terms of n_1, n_2,…, n_r with n_i ≠ ±1 for all i = 1, 2,…,r.
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