nLab
Oka manifold

Oka manifolds comprise a special class of complex analytic manifolds which are suited to apply the Oka principle. Oka maps are a relative version; they are fibrations in the Jardine-Lárusson model structure on the category of simplicial presheaves on the simplicial Stein site. Those cofibrant objects which are representable by complex manifolds are in fact Stein manifolds.

• Franc Forstnerič, Oka manifolds, C. R. Math. Acad. Sci. Paris 347 (2009), 1017–20.
• Franc Forstnerič, Oka maps, arxiv/0911.3439

A beginner’s survey is

• Finnur Lárusson, What is an Oka manifold, Notices AMS, pdf