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  • Book
  • © 2011

Stein Manifolds and Holomorphic Mappings

The Homotopy Principle in Complex Analysis

  • 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

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Table of contents (9 chapters)

  1. Front Matter

    Pages I-XII
  2. Preliminaries

    • Franc Forstnerič
    Pages 1-42
  3. Stein Manifolds

    • Franc Forstnerič
    Pages 43-56
  4. Automorphisms of Complex Euclidean Spaces

    • Franc Forstnerič
    Pages 99-184
  5. Oka Manifolds

    • Franc Forstnerič
    Pages 185-240
  6. Elliptic Complex Geometry and Oka Principle

    • Franc Forstnerič
    Pages 241-290
  7. Applications

    • Franc Forstnerič
    Pages 291-332
  8. Embeddings, Immersions and Submersions

    • Franc Forstnerič
    Pages 333-400
  9. Topological Methods in Stein Geometry

    • Franc Forstnerič
    Pages 401-460
  10. Back Matter

    Pages 461-489

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

  • Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia

    Franc Forstnerič

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

Buy it now

Buying options

eBook USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access