Overview
- Contains a complete and up-to-date account of Oka theory, including the Oka-Grauert theory
- Introduces the theory of holomorphic automorphisms of complex Euclidean spaces in detail
- Presents numerous 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 (10 chapters)
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Front Matter
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Stein Manifolds
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Front Matter
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Back Matter
Keywords
- Stein manifold
- Oka manifold
- elliptic manifold
- holomorphic map
- holomorphic automorphism
- holomorphic fibre bundle
- Oka-Grauert principle
- homotopy principle
- holomorphic spray
- homotopy equivalence
- Stein spaces
- Stein neighborhoods
- Oka theory applications
- complex manifolds flexibility properties
- holomorphic maps flexibility properties
- Stein geometry topological methods
- 32E10, 32H02, 32L05, 32M12, 32M17, 14M17, 58D15
About this book
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.
Authors and Affiliations
About the author
Franc Forstneric has published more than a hundred 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., J. Eur. Math. Soc., Amer. J. Math., and others.
He held long term teaching and research positions at the
University of Wisconsin-Madison (Madison, USA),
Centre for Advanced Study (Oslo, Norway),
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 a hundred 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 and Arts 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/10.1007/978-3-319-61058-0
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing AG 2017
Hardcover ISBN: 978-3-319-61057-3Published: 13 September 2017
Softcover ISBN: 978-3-319-86994-0Published: 11 August 2018
eBook ISBN: 978-3-319-61058-0Published: 05 September 2017
Series ISSN: 0071-1136
Series E-ISSN: 2197-5655
Edition Number: 2
Number of Pages: XV, 562
Number of Illustrations: 28 b/w illustrations, 1 illustrations in colour
Additional Information: Originally published by Springer-Verlag Berlin Heidelberg, 2011
Topics: Functions of a Complex Variable, Global Analysis and Analysis on Manifolds, Several Complex Variables and Analytic Spaces