  We prove a theorem of M. Gromov (Oka's principle for holomorphic sections of
elliptic bundles, J. Amer. Math. Soc. 2, 851-897, 1989) to the effect that
sections of certain holomorphic submersions h from a complex manifold Z onto a
Stein manifold X satisfy the Oka principle, meaning that the inclusion of the
space of holomorphic sections into the space of continuous sections is a weak
homotopy equivalence. The Oka principle holds if the submersion admits a
fiber-dominating spray over a small neighborhood of any point in X. This
extends a classical result of Grauert (Holomorphe Funktionen mit Werten in
komplexen Lieschen Gruppen, Math. Ann. 133, 450-472, 1957). Gromov's result has
been used in the proof of the embedding theorems for Stein manifolds and Stein
spaces into Euclidean spaces of minimal dimension (Y. Eliashberg and M. Gromov,
Ann. Math. 136, 123-135, 1992; J. Schurmann, Math. Ann. 307, 381-399, 1997).
For further extensions see the preprints math.CV/0101034, math.CV/0107039, and
math.CV/0110201.
