Embeddings, Immersions and Submersions

Abstract

In this chapter we study holomorphic immersion, embeddings, and submersions of Stein manifolds to Euclidean spaces and to certain other complex manifolds. The main results include the optimal embedding and immersion theorem for Stein manifolds and finite dimensional Stein spaces to Euclidean spaces, the homotopy principle for holomorphic immersions of Stein manifolds to Euclidean spaces, the Oka principle for proper holomorphic maps of strongly pseudoconvex Stein domains to q-convex manifolds, the construction of proper holomorphic embeddings of certain open Riemann surfaces into ℂ², the construction of noncritical holomorphic functions on Stein manifolds, the homotopy principle for holomorphic submersions of Stein manifolds to Euclidean spaces, and the construction of nonsingular holomorphic foliations on Stein manifolds.