Surjective Holomorphic Maps onto Oka Manifolds

Abstract

Let X be a connected Oka manifold, and let S be a Stein manifold with dimS ≥ dimX. We show that every continuous map S → X is homotopic to a surjective strongly dominating holomorphic map S → X. We also find strongly dominating algebraic morphisms from the affine n-space onto any compact n-dimensional algebraically subelliptic manifold. Motivated by these results, we propose a new holomorphic flexibility property of complex manifolds, the basic Oka property with surjectivity, which could potentially provide another characterization of the class of Oka manifolds.