Naive Kink Equivalence and Doubles of Essential Definite Surfaces

Abstract

Spanning surfaces are fundamental objects in the study of knots, and there are a number of operations that can be performed on spanning surfaces to produce other spanning surfaces. Some of these- kinking and tubing moves- also preserve the underlying knot, and all spanning surfaces can be expressed as the result of applying a series of kinking and tubing moves to an underlying "essential" surface. This paper addresses two questions associated to spanning surfaces.