Stein Manifolds and Holomorphic Mappings

The Homotopy Principle in Complex Analysis

  • Franc Forstnerič

Table of contents

  1. Front Matter
    Pages I-XII
  2. Franc Forstnerič
    Pages 1-42
  3. Franc Forstnerič
    Pages 43-56
  4. Franc Forstnerič
    Pages 99-184
  5. Franc Forstnerič
    Pages 185-240
  6. Franc Forstnerič
    Pages 241-290
  7. Franc Forstnerič
    Pages 291-332
  8. Franc Forstnerič
    Pages 333-400
  9. 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.


Holomorphic approximation Oka manifolds Stein manifolds Stein spaces

Authors and affiliations

  • Franc Forstnerič
    • 1
  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

Bibliographic information