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

  • 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
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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.

About the authors

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

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)

Table of contents (9 chapters)

Buy this book

eBook $149.00
price for USA (gross)
  • ISBN 978-3-642-22250-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $189.00
price for USA
  • ISBN 978-3-642-22249-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $189.00
price for USA
  • ISBN 978-3-642-27032-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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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
2011
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-22250-4
DOI
10.1007/978-3-642-22250-4
Hardcover ISBN
978-3-642-22249-8
Softcover ISBN
978-3-642-27032-1
Series ISSN
0071-1136
Edition Number
1
Number of Pages
XII, 492
Topics