Symplectic 4-Manifolds and Algebraic Surfaces - 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 4-Manifolds and Algebraic Surfaces write by Denis Auroux. This book was released on 2008-04-17. Symplectic 4-Manifolds and Algebraic Surfaces available in PDF, EPUB and Kindle. Modern approaches to the study of symplectic 4-manifolds and algebraic surfaces combine a wide range of techniques and sources of inspiration. Gauge theory, symplectic geometry, pseudoholomorphic curves, singularity theory, moduli spaces, braid groups, monodromy, in addition to classical topology and algebraic geometry, combine to make this one of the most vibrant and active areas of research in mathematics. It is our hope that the five lectures of the present volume given at the C.I.M.E. Summer School held in Cetraro, Italy, September 2-10, 2003 will be useful to people working in related areas of mathematics and will become standard references on these topics. The volume is a coherent exposition of an active field of current research focusing on the introduction of new methods for the study of moduli spaces of complex structures on algebraic surfaces, and for the investigation of symplectic topology in dimension 4 and higher.
Algebraic Surfaces and Holomorphic Vector Bundles
Algebraic Surfaces and Holomorphic Vector Bundles - 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 Algebraic Surfaces and Holomorphic Vector Bundles write by Robert Friedman. This book was released on 2012-12-06. Algebraic Surfaces and Holomorphic Vector Bundles available in PDF, EPUB and Kindle. A novel feature of the book is its integrated approach to algebraic surface theory and the study of vector bundle theory on both curves and surfaces. While the two subjects remain separate through the first few chapters, they become much more tightly interconnected as the book progresses. Thus vector bundles over curves are studied to understand ruled surfaces, and then reappear in the proof of Bogomolov's inequality for stable bundles, which is itself applied to study canonical embeddings of surfaces via Reider's method. Similarly, ruled and elliptic surfaces are discussed in detail, before the geometry of vector bundles over such surfaces is analysed. Many of the results on vector bundles appear for the first time in book form, backed by many examples, both of surfaces and vector bundles, and over 100 exercises forming an integral part of the text. Aimed at graduates with a thorough first-year course in algebraic geometry, as well as more advanced students and researchers in the areas of algebraic geometry, gauge theory, or 4-manifold topology, many of the results on vector bundles will also be of interest to physicists studying string theory.
J-holomorphic Curves and Symplectic Topology
J-holomorphic Curves and Symplectic Topology - 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 J-holomorphic Curves and Symplectic Topology write by Dusa McDuff. This book was released on 2012. J-holomorphic Curves and Symplectic Topology available in PDF, EPUB and Kindle. The main goal of this book is to establish the fundamental theorems of the subject in full and rigourous detail. In particular, the book contains complete proofs of Gromov's compactness theorem for spheres, of the gluing theorem for spheres, and of the associatively of quantum multiplication in the semipositive case. The book can also serve as an introduction to current work in symplectic topology.
Lectures on Symplectic Geometry
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.
Holomorphic Curves in Low Dimensions
Holomorphic Curves in Low Dimensions - 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 Holomorphic Curves in Low Dimensions write by Chris Wendl. This book was released on 2018-06-28. Holomorphic Curves in Low Dimensions available in PDF, EPUB and Kindle. This monograph provides an accessible introduction to the applications of pseudoholomorphic curves in symplectic and contact geometry, with emphasis on dimensions four and three. The first half of the book focuses on McDuff's characterization of symplectic rational and ruled surfaces, one of the classic early applications of holomorphic curve theory. The proof presented here uses the language of Lefschetz fibrations and pencils, thus it includes some background on these topics, in addition to a survey of the required analytical results on holomorphic curves. Emphasizing applications rather than technical results, the analytical survey mostly refers to other sources for proofs, while aiming to provide precise statements that are widely applicable, plus some informal discussion of the analytical ideas behind them. The second half of the book then extends this program in two complementary directions: (1) a gentle introduction to Gromov-Witten theory and complete proof of the classification of uniruled symplectic 4-manifolds; and (2) a survey of punctured holomorphic curves and their applications to questions from 3-dimensional contact topology, such as classifying the symplectic fillings of planar contact manifolds. This book will be particularly useful to graduate students and researchers who have basic literacy in symplectic geometry and algebraic topology, and would like to learn how to apply standard techniques from holomorphic curve theory without dwelling more than necessary on the analytical details. This book is also part of the Virtual Series on Symplectic Geometry http://www.springer.com/series/16019
