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Let F be an oriented surface of genus g with r boundary components and n distinguished points. The mapping class group F= F (F) is 7ro (Diff+ F) where Diff § is the topological group of orientation preserving diffeomorphisms of F which fix the n points and restrict to the identity on~ F. It is known [9] that Hx (F)= 0 for g> 3. In this paper we shall prove the