Abstract
We give a formula for the Casson knot invariant of a p-periodic knot in S3 whose quotient link is a 2-bridge link with Conway's normal form C(2, 2n1, -2, 2n2, …, 2n2m, 2) via the integers p, n1, n2, …, n2m(p ≥ 2 and m ≥ 1). As an application, for any integers n1, n2, ≥, n2m with the same sign, we determine the Δ-unknotting number of a p-periodic knot in S3 whose quotient is a 2-bridge link C(2, 2n1, -2, 2n2, ≥, 2n2m, 2) in terms of p, n1, n2, ≥, n2m. In addition, a recurrence formula for calculating the Alexander polynomial of the 2-bridge knot with Conway's normal form C(2n1, 2n2, ≥, 2nm) via the integers n1,n2, ≥, nm is included.
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