Cobordism distance on the projective space of the knot concordance group

The cobordism distance on the knot concordance group is used to define a measure of how close two knots are to being linearly dependent. Roughly stated, d(K,J) is defined by minimizing the cobordism distance between pairs of knots in cyclic subgroups containing K and J. When made precise, this leads to the definition of the projective space of the knot concordance group. We explore basic properties of this projective space and its integer-valued metric by considering torus knots. Twist knots are used to show that the associated simplicial complex contains an infinite set of simplices of arbitrarily large dimension.