Stein manifolds and holomorphic mappings: the homotopy principle in complex analysis

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 andSeiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary. First systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces. First complete account of Oka-Grauert theory and its modern extensions. Contains a wide variety of applicationsranging from classical to contemporary. INDICE: Preliminaries. - Stein Manifolds. - Stein Neighborhoods and Holomorphic Approximation. - Automorphisms of Complex Euclidean Spaces. - Oka Manifolds. - Elliptic Complex Geometry and Oka Principle. - Applications. - Embeddings, Immersions and Submersions. Topological Methods in Stein Geometry. - References. - Index.

• ISBN: 978-3-642-22249-8
• Editorial: Springer
• Encuadernacion: Cartoné
• Páginas: 492
• Fecha Publicación: 31/08/2011
• Nº Volúmenes: 1
• Idioma: Inglés