Finite-dimensional complex manifolds on commutative Banach algebras and continuous families of compact complex manifolds

Abstract

Let Γ(M) be the set of all global continuous cross sections of a continuous family M of compact complex manifolds on a compact Hausdorff space X. In this paper, we introduce a C(X)-manifold structure on Γ(M). Especially, if X is contractible, then Γ(M) is a finite-dimensional C(X)-manifold. Here, C(X) denotes the Banach algebra of all complex-valued continuous functions on X.

Keywords

• topological deformation of complex analytic structures
• infinite-dimensional manifold
• commutative c*-algebra
• serre-swan theorem
• 19l99
• 32q99
• 46j99
• 58b99