Overview
- 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 applications ranging from classical to contemporary
- Includes supplementary material: sn.pub/extras
Part of the book series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics (MATHE3, volume 56)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
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)Authors and Affiliations
About the author
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
Bibliographic Information
Book Title: Stein Manifolds and Holomorphic Mappings
Book Subtitle: The Homotopy Principle in Complex Analysis
Authors: Franc Forstnerič
Series Title: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
DOI: https://doi.org/10.1007/978-3-642-22250-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2011
Hardcover ISBN: 978-3-642-22249-8Published: 28 August 2011
eBook ISBN: 978-3-642-22250-4Published: 27 August 2011
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 1
Number of Pages: XII, 492