Riemannian Geometry of Contact and Symplectic Manifolds - 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 Riemannian Geometry of Contact and Symplectic Manifolds write by David E. Blair. This book was released on 2013-11-11. Riemannian Geometry of Contact and Symplectic Manifolds available in PDF, EPUB and Kindle. Book endorsed by the Sunyer Prize Committee (A. Weinstein, J. Oesterle et. al.).
An Introduction to Symplectic Geometry
An Introduction to 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 An Introduction to Symplectic Geometry write by Rolf Berndt. This book was released on 2001. An Introduction to Symplectic Geometry available in PDF, EPUB and Kindle. Symplectic geometry is a central topic of current research in mathematics. Indeed, symplectic methods are key ingredients in the study of dynamical systems, differential equations, algebraic geometry, topology, mathematical physics and representations of Lie groups. This book is a true introduction to symplectic geometry, assuming only a general background in analysis and familiarity with linear algebra. It starts with the basics of the geometry of symplectic vector spaces. Then, symplectic manifolds are defined and explored. In addition to the essential classic results, such as Darboux's theorem, more recent results and ideas are also included here, such as symplectic capacity and pseudoholomorphic curves. These ideas have revolutionized the subject. The main examples of symplectic manifolds are given, including the cotangent bundle, Kähler manifolds, and coadjoint orbits. Further principal ideas are carefully examined, such as Hamiltonian vector fields, the Poisson bracket, and connections with contact manifolds. Berndt describes some of the close connections between symplectic geometry and mathematical physics in the last two chapters of the book. In particular, the moment map is defined and explored, both mathematically and in its relation to physics. He also introduces symplectic reduction, which is an important tool for reducing the number of variables in a physical system and for constructing new symplectic manifolds from old. The final chapter is on quantization, which uses symplectic methods to take classical mechanics to quantum mechanics. This section includes a discussion of the Heisenberg group and the Weil (or metaplectic) representation of the symplectic group. Several appendices provide background material on vector bundles, on cohomology, and on Lie groups and Lie algebras and their representations. Berndt's presentation of symplectic geometry is a clear and concise introduction to the major methods and applications of the subject, and requires only a minimum of prerequisites. This book would be an excellent text for a graduate course or as a source for anyone who wishes to learn about symplectic geometry.
Contact and Symplectic Topology
Contact 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 Contact and Symplectic Topology write by Frédéric Bourgeois. This book was released on 2014-03-10. Contact and Symplectic Topology available in PDF, EPUB and Kindle. Symplectic and contact geometry naturally emerged from the mathematical description of classical physics. The discovery of new rigidity phenomena and properties satisfied by these geometric structures launched a new research field worldwide. The intense activity of many European research groups in this field is reflected by the ESF Research Networking Programme "Contact And Symplectic Topology" (CAST). The lectures of the Summer School in Nantes (June 2011) and of the CAST Summer School in Budapest (July 2012) provide a nice panorama of many aspects of the present status of contact and symplectic topology. The notes of the minicourses offer a gentle introduction to topics which have developed in an amazing speed in the recent past. These topics include 3-dimensional and higher dimensional contact topology, Fukaya categories, asymptotically holomorphic methods in contact topology, bordered Floer homology, embedded contact homology, and flexibility results for Stein manifolds.
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.
Symplectic and Contact Geometry
Symplectic and Contact 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 Symplectic and Contact Geometry write by Anahita Eslami Rad. This book was released on . Symplectic and Contact Geometry available in PDF, EPUB and Kindle.
