Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis (Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics Book 56)

None. The Ergebnisse volumes do not have back cover texts. The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary. Front Matter....Pages I-XII Preliminaries....Pages 1-42 Stein Manifolds....Pages 43-56 Stein Neighborhoods and Holomorphic Approximation....Pages 57-98 Automorphisms of Complex Euclidean Spaces....Pages 99-184 Oka Manifolds....Pages 185-240 Elliptic Complex Geometry and Oka Principle....Pages 241-290 Applications....Pages 291-332 Embeddings, Immersions and Submersions....Pages 333-400 Topological Methods in Stein Geometry....Pages 401-460 Back Matter....Pages 461-489