We translate the problem of finding the self-intersections of an evolving loop of cosmic string into a topological problem. We use this picture to discuss the relationship between cusps and self-intersections and give a lower bound on the total number of self-intersections any particular loop can have. This bound can be calculated by studying only the kinks and cusps present on the loop. We discuss the ways in which the number of cusps and self-intersections can change under smooth deformations of the initial conditions.

• Received 25 March 1988

DOI:https://doi.org/10.1103/PhysRevD.38.2958