Vector bundles over holomorphic manifolds on locally convex spaces (Q1038539)

In this paper a general theory of vector bundles over holomorphic manifolds \(M\) modeled on locally convex spaces \(E\) is developed. One starts with a set \(P\) and a surjection \(\pi\) from \(P\) to \(M\) and one introduces the notion of vector bundle atlas (patch) with fiber space \(F\) as in the book of [\textit{S. Lang}, Fundamentals of differential geometry. Graduate Texts in Mathematics. 191. New York, NY: Springer. (1999; Zbl 0932.53001)]. One proves that \(P\) as total space becomes a holomorphic manifold modeled on \(E\times F\) and \(\pi\) becomes a submersion. Then one defines the vector bundle morphisms, and the usual constructions in the category of vector bundles (restrictions, subbundles, quotient, direct product direct sum) are described.