Elliptic characterization and unification of Oka maps

Abstract

We generalize our elliptic characterization of Oka manifolds to Oka maps. The generalized characterization can be considered as an affirmative answer to the relative version of Gromov's conjecture. As an application, we unify previously known Oka principles for submersions; namely the Gromov type Oka principle for subelliptic submersions and the Forstnerič type Oka principle for holomorphic fiber bundles with CAP fibers. We also establish the localization principle for Oka maps which gives new examples of Oka maps.

19 pages

References in corpus (2)

• An implicit function theorem for sprays and applications to Oka theory
• Oka complements of countable sets and non-elliptic Oka manifolds

Cited by in corpus (2)

• Recent developments on Oka manifolds
• Oka tubes in holomorphic line bundles