An Algorithm for Simple Curves on Surfaces
Joan S. Birman, Caroline Series · Journal of the London Mathematical Society · 1984
Let M be a compact orientable surface with non-empty boundary and with X{M) < 0, and let T = nlM. Let C be the free homotopy class of a closed loop on M and let W = W{C) be a word in a fixed set of generators T which represents C. In this paper we give an algorithm to decide, starting with W, whether C has a simple