Stein Manifolds and Holomorphic Mappings

The Homotopy Principle in Complex Analysis

By: Franc Forstneri?

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Hardcover | 28 August 2011

At a Glance

Hardcover
506 Pages

Dimensions(cm)
23.39 x 15.6 x 2.87

Hardcover

$243.04

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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.

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"The main focus of the book is the theory of the Oka principle, which has been extensively developed in the past decade following a seminal paper of Gromov in 1989. ... The book can serve as a textbook for advanced graduate students specialising in complex geometry, as a reference for researchers in the field, and as an accessible resource for people in related areas. The book truly fills a gap in the literature. ... a standard reference for years to come." (Finnur Larusson, Mathematical Reviews, May, 2013)

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