Volume 15, issue 5 (2015)

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Torus knots obtained by twisting torus knots

Sangyop Lee

Algebraic & Geometric Topology 15 (2015) 2817–2836
Abstract

A twisted torus knot is obtained from a torus knot by adding a number of full twists to some adjacent strands of the torus knot. In this paper, we show that if a twisted torus knot is a torus knot, then the number of added full twists is generically at most two in absolute value. We also show that this bound is the best possible by classifying twisted torus knots for which the upper bound is attained.

Keywords
Dehn surgery, torus knots, twisted torus knots
Primary: 57N10