Symplectic Manifolds with no Kaehler structure

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Release : 2006-11-14
Genre : Mathematics
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Book Rating : 456/5 ( reviews)

Symplectic Manifolds with no Kaehler structure - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Symplectic Manifolds with no Kaehler structure write by Alesky Tralle. This book was released on 2006-11-14. Symplectic Manifolds with no Kaehler structure available in PDF, EPUB and Kindle. This is a research monograph covering the majority of known results on the problem of constructing compact symplectic manifolds with no Kaehler structure with an emphasis on the use of rational homotopy theory. In recent years, some new and stimulating conjectures and problems have been formulated due to an influx of homotopical ideas. Examples include the Lupton-Oprea conjecture, the Benson-Gordon conjecture, both of which are in the spirit of some older and still unsolved problems (e.g. Thurston's conjecture and Sullivan's problem). Our explicit aim is to clarify the interrelations between certain aspects of symplectic geometry and homotopy theory in the framework of the problems mentioned above. We expect that the reader is aware of the basics of differential geometry and algebraic topology at graduate level.

Lectures on Symplectic Geometry

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Release : 2004-10-27
Genre : Mathematics
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Book Rating : 30X/5 ( reviews)

Lectures on Symplectic Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Symplectic Geometry write by Ana Cannas da Silva. This book was released on 2004-10-27. Lectures on Symplectic Geometry available in PDF, EPUB and Kindle. The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Collected Works of William P. Thurston with Commentary

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Release : 2023-06-05
Genre : Mathematics
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Book Rating : 727/5 ( reviews)

Collected Works of William P. Thurston with Commentary - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Collected Works of William P. Thurston with Commentary write by Benson Farb. This book was released on 2023-06-05. Collected Works of William P. Thurston with Commentary available in PDF, EPUB and Kindle. William Thurston's work has had a profound influence on mathematics. He connected whole mathematical subjects in entirely new ways and changed the way mathematicians think about geometry, topology, foliations, group theory, dynamical systems, and the way these areas interact. His emphasis on understanding and imagination in mathematical learning and thinking are integral elements of his distinctive legacy. This four-part collection brings together in one place Thurston's major writings, many of which are appearing in publication for the first time. Volumes I–III contain commentaries by the Editors. Volume IV includes a preface by Steven P. Kerckhoff. Volume I contains William Thurston's papers on foliations, mapping classes groups, and differential geometry.

An Introduction to Extremal Kahler Metrics

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Release : 2014-06-19
Genre : Mathematics
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Book Rating : 478/5 ( reviews)

An Introduction to Extremal Kahler Metrics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Extremal Kahler Metrics write by Gábor Székelyhidi. This book was released on 2014-06-19. An Introduction to Extremal Kahler Metrics available in PDF, EPUB and Kindle. A basic problem in differential geometry is to find canonical metrics on manifolds. The best known example of this is the classical uniformization theorem for Riemann surfaces. Extremal metrics were introduced by Calabi as an attempt at finding a higher-dimensional generalization of this result, in the setting of Kähler geometry. This book gives an introduction to the study of extremal Kähler metrics and in particular to the conjectural picture relating the existence of extremal metrics on projective manifolds to the stability of the underlying manifold in the sense of algebraic geometry. The book addresses some of the basic ideas on both the analytic and the algebraic sides of this picture. An overview is given of much of the necessary background material, such as basic Kähler geometry, moment maps, and geometric invariant theory. Beyond the basic definitions and properties of extremal metrics, several highlights of the theory are discussed at a level accessible to graduate students: Yau's theorem on the existence of Kähler-Einstein metrics, the Bergman kernel expansion due to Tian, Donaldson's lower bound for the Calabi energy, and Arezzo-Pacard's existence theorem for constant scalar curvature Kähler metrics on blow-ups.

Lectures on Kähler Geometry

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Release : 2007-03-29
Genre : Mathematics
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Book Rating : 004/5 ( reviews)

Lectures on Kähler Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Lectures on Kähler Geometry write by Andrei Moroianu. This book was released on 2007-03-29. Lectures on Kähler Geometry available in PDF, EPUB and Kindle. Kähler geometry is a beautiful and intriguing area of mathematics, of substantial research interest to both mathematicians and physicists. This self-contained graduate text provides a concise and accessible introduction to the topic. The book begins with a review of basic differential geometry, before moving on to a description of complex manifolds and holomorphic vector bundles. Kähler manifolds are discussed from the point of view of Riemannian geometry, and Hodge and Dolbeault theories are outlined, together with a simple proof of the famous Kähler identities. The final part of the text studies several aspects of compact Kähler manifolds: the Calabi conjecture, Weitzenböck techniques, Calabi–Yau manifolds, and divisors. All sections of the book end with a series of exercises and students and researchers working in the fields of algebraic and differential geometry and theoretical physics will find that the book provides them with a sound understanding of this theory.