Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics

Stein Manifolds and Holomorphic Mappings

The Homotopy Principle in Complex Analysis

Authors: Forstnerič, Franc

  • 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
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About this book

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.

About the authors

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.

Table of contents (10 chapters)

Buy this book

eBook 107,09 €
price for Spain (gross)
  • ISBN 978-3-319-61058-0
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 135,19 €
price for Spain (gross)
  • ISBN 978-3-319-61057-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Stein Manifolds and Holomorphic Mappings
Book Subtitle
The Homotopy Principle in Complex Analysis
Authors
Series Title
Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics
Series Volume
56
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-61058-0
DOI
10.1007/978-3-319-61058-0
Hardcover ISBN
978-3-319-61057-3
Series ISSN
0071-1136
Edition Number
2
Number of Pages
XV, 562
Number of Illustrations and Tables
28 b/w illustrations, 1 illustrations in colour
Additional Information
Originally published by Springer-Verlag Berlin Heidelberg, 2011
Topics