A complex manifold X is called taut if Hol (D,X) is a normal familiy, where D denotes the unit disk. Let Tn denote the set of all complex taut manifolds of dimension n with assigned basepoint (up to biholomorphic equivalence). By a result of Ma, Tn may be equipped with the structure of a metric topological space. We show that the Betti-Numbers of the taut manifolds give lower-semicontinuous functions on Tn. Moreover each two taut manifolds X, Y in the same connected component of Tn are homotopy-equivalent. This is achieved by associating "minimal models" to taut manifolds. Examples are given of connected subsets of Tn such that the corresponding taut manifolds are topologically non-trivial.
International Journal of Mathematics 8 , 149-168 (1997)