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

ISBN-13: 9783319869940 / Angielski / Miękka / 2018 / 562 str.

Franc Forstnerič

Opis

The theme of this book is an examination of the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds, offering the first complete account of Oka-Grauert theory and its modern extensions.

Spis treści

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.

O autorze

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.