On Compact Analytic Surfaces

THEOREM 11.1. The family 9(,{, G) consists of all analytic fibre spaces Bi, '2C H'(A, f2(B#)). The notion of fibre spaces and their equivalences depends on the sheaf of structure groups.' By a (63-fibre space we mean a fibre space with a sheaf (3 of structure groups, and we say that two fibre spaces are (X-equivalent if they are equivalent as (63-fibre spaces. The fibre space Bi may be considered as an analytic fibre space, as an f2(BO)-fibre space, or as an f2(Bl)-fibre space. The cohomology class C) C H'(Ay, f(BO)) represents the f2(Bl)-equivalence class of Be. Let C& denote the fibre of BI over u c A. It is clear that