Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis
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.
1133679038
Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis
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.
199.99 In Stock
Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis

Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis

by Franc Forstneric
Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis

Stein Manifolds and Holomorphic Mappings: The Homotopy Principle in Complex Analysis

by Franc Forstneric

Hardcover(2nd ed. 2017)

$199.99 
  • SHIP THIS ITEM
    In stock. Ships in 1-2 days.
    Not Eligible for Free Shipping
  • PICK UP IN STORE

    Your local store may have stock of this item.

Related collections and offers


Overview

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.

Product Details

ISBN-13: 9783319610573
Publisher: Springer International Publishing
Publication date: 09/07/2017
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathematics , #56
Edition description: 2nd ed. 2017
Pages: 562
Product dimensions: 6.10(w) x 9.25(h) x (d)

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 (Skholm, 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

Table of Contents

Part I Stein Manifolds.- 1 Preliminaries.- 2 Stein Manifolds.- 3 Stein Neighborhoods and Approximation.- 4 Automorphisms of Complex Euclidean Spaces.- Part II Oka Theory.- 5 Oka Manifolds.- 6 Elliptic Complex Geometry and Oka Theory.- 7 Flexibility Properties of Complex Manifolds and Holomorphic Maps.- Part III Applications.- 8 Applications of Oka Theory and its Methods.- 9 Embeddings, Immersions and Submersions.- 10 Topological Methods in Stein Geometry.- References.- Index.

From the B&N Reads Blog

Customer Reviews