Abstract. We give a complete classification of homotopy classes of partial isometries in von Neumann algebras (Theorem 3.1). This classification is particularly explicit in the case of factors (Section 4) and generalizes and explains the results obtained in [3] for type I factors.

AMS Subject Classification (1991): 46L10, 46L35, 47A05

Received November 3, 2000, and in revised form December 5, 2001. (Registered under 2841/2009.)