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Stein Manifolds and Holomorphic Mappings

The Homotopy Principle in Complex Analysis

Franc Forstnerič (Autor)

Buch | Hardcover

XII, 492 Seiten

2011 | 2011
Springer Berlin (Verlag)
978-3-642-22249-8 (ISBN)

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lt;p>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.

Franc Forstneric has published close to eighty research and survey papers in complex analysis and geometry, including several in leading mathematical journals such as the Annals of Math., Acta Math., Inventiones Math., Duke Math. J., Amer. J. Math., Math. Ann., and others. He held long term teaching and research positions at the University of Wisconsin-Madison (Madison, USA), Institut Mittag-Leffler (Stockholm, Sweden), Max Planck Institute (Bonn, Germany), as well as visiting positions at more than ten other institutions. He was an invited speaker at over 70 international conferences and workshops. Since 2000 he is a Professor of Mathematics at the University of Ljubljana and is a member of the Academy of Sciences of the Republic of Slovenia

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.

lt;p>From the reviews:

"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 Lárusson, Mathematical Reviews, May, 2013)

Erscheint lt. Verlag	28.8.2011
Reihe/Serie	Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Zusatzinfo	XII, 492 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	881 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Holomorphic approximation • Oka manifolds • Stein manifolds • Stein spaces
ISBN-10	3-642-22249-8 / 3642222498
ISBN-13	978-3-642-22249-8 / 9783642222498
Zustand	Neuware