Prime knots and concordance

Abstract

This paper proves that any knot is concordant to a prime knot; it thus solves Problem 13 of (3). In doing so it makes an exploration of a fairly general method of proving that a knot is a prime. Throughout, the word ‘knot’ means a knot of S1 in S3 (orientations being here irrelevant); occasionally reference will be made to the idea of a knotted arc spanning a 3-ball.