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Author: Franc Forstnerič
Publisher: Springer
ISBN: 3319610589
Category : Mathematics
Languages : en
Pages : 569
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Book Description
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.
Author: Franc Forstnerič
Publisher: Springer
ISBN: 3319610589
Category : Mathematics
Languages : en
Pages : 569
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Book Description
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.
Author: Kai Cieliebak
Publisher: American Mathematical Soc.
ISBN: 0821885332
Category : Mathematics
Languages : en
Pages : 379
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Book Description
This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine complex (a.k.a. Stein) manifolds have canonically built into them symplectic geometry which is responsible for many phenomena in complex geometry and analysis. The goal of the book is the exploration of this symplectic geometry (the road from 'Stein to Weinstein') and its applications in the complex geometric world of Stein manifolds (the road 'back').
Author: Burak Ozbagci
Publisher: Springer Science & Business Media
ISBN: 366210167X
Category : Mathematics
Languages : en
Pages : 279
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Book Description
This book is about an investigation of recent developments in the field of sympletic and contact structures on four- and three-dimensional manifolds from a topologist’s point of view. In it, two main issues are addressed: what kind of sympletic and contact structures we can construct via surgery theory and what kind of sympletic and contact structures are not allowed via gauge theory and the newly invented Heegaard-Floer theory.
Author: John M. Lee
Publisher: American Mathematical Society
ISBN: 1470476959
Category : Mathematics
Languages : en
Pages : 377
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Book Description
Complex manifolds are smooth manifolds endowed with coordinate charts that overlap holomorphically. They have deep and beautiful applications in many areas of mathematics. This book is an introduction to the concepts, techniques, and main results about complex manifolds (mainly compact ones), and it tells a story. Starting from familiarity with smooth manifolds and Riemannian geometry, it gradually explains what is different about complex manifolds and develops most of the main tools for working with them, using the Kodaira embedding theorem as a motivating project throughout. The approach and style will be familiar to readers of the author's previous graduate texts: new concepts are introduced gently, with as much intuition and motivation as possible, always relating new concepts to familiar old ones, with plenty of examples. The main prerequisite is familiarity with the basic results on topological, smooth, and Riemannian manifolds. The book is intended for graduate students and researchers in differential geometry, but it will also be appreciated by students of algebraic geometry who wish to understand the motivations, analogies, and analytic results that come from the world of differential geometry.
Author: Robert E. Gompf
Publisher: American Mathematical Soc.
ISBN: 0821809946
Category : Mathematics
Languages : en
Pages : 576
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Book Description
Presents an exposition of Kirby calculus, or handle body theory on 4-manifolds. This book includes such topics as branched coverings and the geography of complex surfaces, elliptic and Lefschetz fibrations, $h$-cobordisms, symplectic 4-manifolds, and Stein surfaces.
Author: Steven Bell
Publisher: Springer Science & Business Media
ISBN: 9783540629955
Category : Mathematics
Languages : en
Pages : 324
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Book Description
The articles in this volume were written to commemorate Reinhold Remmert's 60th birthday in June, 1990. They are surveys, meant to facilitate access to some of the many aspects of the theory of complex manifolds, and demonstrate the interplay between complex analysis and many other branches of mathematics, algebraic geometry, differential topology, representations of Lie groups, and mathematical physics being only the most obvious of these branches. Each of these articles should serve not only to describe the particular circle of ideas in complex analysis with which it deals but also as a guide to the many mathematical ideas related to its theme.
Author: E.M. Chirka
Publisher: Springer Science & Business Media
ISBN: 3642615252
Category : Mathematics
Languages : en
Pages : 252
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Book Description
From the reviews: "... In sum, the volume under review is the first quarter of an important work that surveys an active branch of modern mathematics. Some of the individual articles are reminiscent in style of the early volumes of the first Ergebnisse series and will probably prove to be equally useful as a reference; ...for the appropriate reader, they will be valuable sources of information about modern complex analysis." Bulletin of the Am.Math.Society, 1991 "... This remarkable book has a helpfully informal style, abundant motivation, outlined proofs followed by precise references, and an extensive bibliography; it will be an invaluable reference and a companion to modern courses on several complex variables." ZAMP, Zeitschrift für Angewandte Mathematik und Physik, 1990
Author: Mark Gross
Publisher: Springer Science & Business Media
ISBN: 3642190049
Category : Mathematics
Languages : en
Pages : 245
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Book Description
This is an introduction to a very active field of research, on the boundary between mathematics and physics. It is aimed at graduate students and researchers in geometry and string theory. Proofs or sketches are given for many important results. From the reviews: "An excellent introduction to current research in the geometry of Calabi-Yau manifolds, hyper-Kähler manifolds, exceptional holonomy and mirror symmetry....This is an excellent and useful book." --MATHEMATICAL REVIEWS
Author: Jisoo Byun
Publisher: Springer
ISBN: 9811316724
Category : Mathematics
Languages : en
Pages : 359
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Book Description
The KSCV Symposium, the Korean Conference on Several Complex Variables, started in 1997 in an effort to promote the study of complex analysis and geometry. Since then, the conference met semi-regularly for about 10 years and then settled on being held biannually. The sixth and tenth conferences were held in 2002 and 2014 as satellite conferences to the Beijing International Congress of Mathematicians (ICM) and the Seoul ICM, respectively. The purpose of the KSCV Symposium is to organize the research talks of many leading scholars in the world, to provide an opportunity for communication, and to promote new researchers in this field.
Author: HENKIN
Publisher: Birkhäuser
ISBN: 3034865376
Category : Science
Languages : en
Pages : 227
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Book Description
