Twisted torus knots T (m n + m + 1, m n + 1, m n + m + 2, - 1) and T (n + 1, n, 2 n - 1, - 1) are torus knots

초록

A twisted torus knot T(p,q,r,s) is a torus knot T(p,q) with r adjacent strands twisted fully s times. In this paper, we determine the braid index of the knot T(p,q,r,s) when the parameters p,q,r satisfy 1 < q < p < r ≤ p + q. If the last parameter s additionally satisfies s = -1, then we also determine the parameters p,q,r for which T(p,q,r,s) is a torus knot. © 2021 World Scientific Publishing Company.

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