Stein Manifolds and Holomorphic Mappings
Franc Forstnerič
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Springer International Publishing
Naturwissenschaften, Medizin, Informatik, Technik / Analysis
Beschreibung
This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds.
Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory.
Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.
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Schlagwörter
Stein neighborhoods, Oka-Grauert principle, holomorphic automorphism, 32E10, 32H02, 32L05, 32M12, 32M17, 14M17, 58D15, Stein spaces, holomorphic spray, Stein manifold, holomorphic fibre bundle, Stein geometry topological methods, holomorphic map, Oka manifold, holomorphic maps flexibility properties, elliptic manifold, complex manifolds flexibility properties, Oka theory applications, homotopy equivalence, homotopy principle