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, connecti…
Read More ↓Title Statements
- Full title :Stein manifolds and holomorphic mappings : the homotopy principle in complex analysis / Franc Forstnerič.
Summary
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.
Read More ↓Edition Statements
- Publication Date:2011.
- Edition:1st ed
Publication Statements
- Publisher(s):Springer
- Place of Publication:New York
- Language:eng
- Publication Date:2011.
The Physical Object
- Description:1 online resource (x, 489 pages) : : illustrations.
Edition Identifiers
- ISBN:9783642222504, 3642222501
- oclc:ocn763157505
- LC Classification:QA331.7
- Dewey Decimal:516.07
Table of Contents
Stein Manifolds and Holomorphic Mappings; Preface; Contents; 1 Preliminaries; 1.1 Complex Manifolds and Holomorphic Mappings; 1.2 Examples of Complex Manifolds; 1.3 Subvarieties and Complex Spaces; 1.4 Holomorphic Fiber Bundles; 1.5 Holomorphic Vector Bundles; 1.6 The Tangent Bundle; 1.7 The Cotangent Bundle and Differential Forms; 1.8 Plurisubharmonic Functions and the Levi Form; 1.9 Vector Fields, Flows and Foliations; 1.10 Jet Bundles, Holonomic Sections and the Homotopy Principle; 2 Stein Manifolds; 2.1 Domains of Holomorphy; 2.2 Stein Manifolds and Stein Spaces
2.3 Characterization by Plurisubharmonic Functions2.4 Cartan-Serre Theorems A & B; 2.5 The partial-Problem; 3 Stein Neighborhoods and Holomorphic Approximation; 3.1 Q-Complete Neighborhoods; 3.2 Stein Neighborhoods of Stein Subvarieties; 3.3 Holomorphic Retractions onto Stein Submanifolds; 3.4 A Semiglobal Holomorphic Extension Theorem; 3.5 Totally Real Submanifolds; 3.6 Stein Neighborhoods of Certain Laminated Sets; 3.7 Stein Compacts with Totally Real Handles; 3.8 Thin Strongly Pseudoconvex Handlebodies; 3.9 Morse Critical Points of q-Convex Functions
3.10 Crossing a Critical Level of a q-Convex Function3.11 The To…
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