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1. Introduction. In this note we announce two theorems. The first describes the homotopy type of the topological group £>(X) of diffeomorphisms ( = C°°-diffeomorphisms) of a compact oriented surface X without boundary. The second, of which the first is a corollary, gives a fundamental relation among £)(X), the space of complex structures on X, and the Teichmüller space T(X) of X. We make essential use of the theory of quasiconformal mappings and Teichmüller spaces developed by Ahlfors and Bers [3], [ó], and the theory of fibrations of function spaces. Our results confirm a conjecture of Grothendieck [7, p. 7-09], relating the homotopy of £)(X) and T(X).

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