Lectures On The Geometry Of Poisson Manifolds

Author : Izu Vaisman
Publisher : Birkhäuser
Page : 210 pages
File Size : 51,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034884952

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Lectures on the Geometry of Poisson Manifolds by Izu Vaisman Pdf

This book is addressed to graduate students and researchers in the fields of mathematics and physics who are interested in mathematical and theoretical physics, differential geometry, mechanics, quantization theories and quantum physics, quantum groups etc., and who are familiar with differentiable and symplectic manifolds. The aim of the book is to provide the reader with a monograph that enables him to study systematically basic and advanced material on the recently developed theory of Poisson manifolds, and that also offers ready access to bibliographical references for the continuation of his study. Until now, most of this material was dispersed in research papers published in many journals and languages. The main subjects treated are the Schouten-Nijenhuis bracket; the generalized Frobenius theorem; the basics of Poisson manifolds; Poisson calculus and cohomology; quantization; Poisson morphisms and reduction; realizations of Poisson manifolds by symplectic manifolds and by symplectic groupoids and Poisson-Lie groups. The book unifies terminology and notation. It also reports on some original developments stemming from the author's work, including new results on Poisson cohomology and geometric quantization, cofoliations and biinvariant Poisson structures on Lie groups.

Author : Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ
Publisher : American Mathematical Soc.
Page : 479 pages
File Size : 40,5 Mb
Release : 2021-10-14
Category : Education
ISBN : 9781470466671

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Lectures on Poisson Geometry by Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ Pdf

This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way. —Alan Weinstein, University of California at Berkeley This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study. —Eckhard Meinrenken, University of Toronto

Author : Marius Crainic,Rui Loja Fernandes,Ioan Mărcuț
Publisher : Unknown
Page : 128 pages
File Size : 42,5 Mb
Release : 1900
Category : Electronic books
ISBN : 147046666X

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Lectures on Poisson Geometry by Marius Crainic,Rui Loja Fernandes,Ioan Mărcuț Pdf

This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way.--Alan Weinstein, University of California at BerkeleyThis well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics.

Author : Izu Vaisman
Publisher : Unknown
Page : 96 pages
File Size : 49,6 Mb
Release : 2000
Category : Differentiable manifolds
ISBN : UOM:39015052046391

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Lectures on Symplectic and Poisson Geometry by Izu Vaisman Pdf

Author : Giuseppe Dito,Jiang-Hua Lu,Yoshiaki Maeda
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 55,7 Mb
Release : 2008
Category : Geometric quantization
ISBN : 9780821844236

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Poisson Geometry in Mathematics and Physics by Giuseppe Dito,Jiang-Hua Lu,Yoshiaki Maeda Pdf

This volume is a collection of articles by speakers at the Poisson 2006 conference. The program for Poisson 2006 was an overlap of topics that included deformation quantization, generalized complex structures, differentiable stacks, normal forms, and group-valued moment maps and reduction.

Author : Liviu I. Nicolaescu
Publisher : World Scientific
Page : 606 pages
File Size : 44,5 Mb
Release : 2007
Category : Mathematics
ISBN : 9789812770295

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Lectures on the Geometry of Manifolds by Liviu I. Nicolaescu Pdf

The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology.The book's guiding philosophy is, in the words of Newton, that "in learning the sciences examples are of more use than precepts". We support all the new concepts by examples and, whenever possible, we tried to present several facets of the same issue.While we present most of the local aspects of classical differential geometry, the book has a "global and analytical bias". We develop many algebraic-topological techniques in the special context of smooth manifolds such as Poincar� duality, Thom isomorphism, intersection theory, characteristic classes and the Gauss-Bonnet theorem.We devoted quite a substantial part of the book to describing the analytic techniques which have played an increasingly important role during the past decades. Thus, the last part of the book discusses elliptic equations, including elliptic Lpand H�lder estimates, Fredholm theory, spectral theory, Hodge theory, and applications of these. The last chapter is an in-depth investigation of a very special, but fundamental class of elliptic operators, namely, the Dirac type operators.The second edition has many new examples and exercises, and an entirely new chapter on classical integral geometry where we describe some mathematical gems which, undeservedly, seem to have disappeared from the contemporary mathematical limelight.

Author : Sean Bates,Alan Weinstein
Publisher : American Mathematical Soc.
Page : 150 pages
File Size : 50,9 Mb
Release : 1997
Category : Mathematics
ISBN : 0821807986

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Lectures on the Geometry of Quantization by Sean Bates,Alan Weinstein Pdf

These notes are based on a course entitled ``Symplectic Geometry and Geometric Quantization'' taught by Alan Weinstein at the University of California, Berkeley (fall 1992) and at the Centre Emile Borel (spring 1994). The only prerequisite for the course needed is a knowledge of the basic notions from the theory of differentiable manifolds (differential forms, vector fields, transversality, etc.). The aim is to give students an introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role these ideas play in formalizing the transition between the mathematics of classical dynamics (hamiltonian flows on symplectic manifolds) and quantum mechanics (unitary flows on Hilbert spaces). These notes are meant to function as a guide to the literature. The authors refer to other sources for many details that are omitted and can be bypassed on a first reading.

Author : Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ
Publisher : American Mathematical Soc.
Page : 479 pages
File Size : 48,7 Mb
Release : 2021-09-14
Category : Education
ISBN : 9781470464301

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Lectures on Poisson Geometry by Marius Crainic,Rui Loja Fernandes,Ioan Mărcuţ Pdf

This excellent book will be very useful for students and researchers wishing to learn the basics of Poisson geometry, as well as for those who know something about the subject but wish to update and deepen their knowledge. The authors' philosophy that Poisson geometry is an amalgam of foliation theory, symplectic geometry, and Lie theory enables them to organize the book in a very coherent way. —Alan Weinstein, University of California at Berkeley This well-written book is an excellent starting point for students and researchers who want to learn about the basics of Poisson geometry. The topics covered are fundamental to the theory and avoid any drift into specialized questions; they are illustrated through a large collection of instructive and interesting exercises. The book is ideal as a graduate textbook on the subject, but also for self-study. —Eckhard Meinrenken, University of Toronto

Author : Iskander Asanovich Taĭmanov
Publisher : European Mathematical Society
Page : 224 pages
File Size : 54,9 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190507

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Lectures on Differential Geometry by Iskander Asanovich Taĭmanov Pdf

Differential geometry studies geometrical objects using analytical methods. Like modern analysis itself, differential geometry originates in classical mechanics. For instance, geodesics and minimal surfaces are defined via variational principles and the curvature of a curve is easily interpreted as the acceleration with respect to the path length parameter. Modern differential geometry in its turn strongly contributed to modern physics. This book gives an introduction to the basics of differential geometry, keeping in mind the natural origin of many geometrical quantities, as well as the applications of differential geometry and its methods to other sciences. The text is divided into three parts. The first part covers the basics of curves and surfaces, while the second part is designed as an introduction to smooth manifolds and Riemannian geometry. In particular, Chapter 5 contains short introductions to hyperbolic geometry and geometrical principles of special relativity theory. Here, only a basic knowledge of algebra, calculus and ordinary differential equations is required. The third part is more advanced and introduces into matrix Lie groups and Lie algebras the representation theory of groups, symplectic and Poisson geometry, and applications of complex analysis in surface theory. The book is based on lectures the author held regularly at Novosibirsk State University. It is addressed to students as well as anyone who wants to learn the basics of differential geometry.

Author : Simone Gutt,John Rawnsley,Daniel Sternheimer
Publisher : Cambridge University Press
Page : 380 pages
File Size : 55,7 Mb
Release : 2005-06-21
Category : Mathematics
ISBN : 0521615054

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Poisson Geometry, Deformation Quantisation and Group Representations by Simone Gutt,John Rawnsley,Daniel Sternheimer Pdf

An accessible introduction to Poisson geometry suitable for graduate students.

Author : Liviu I Nicolaescu
Publisher : World Scientific
Page : 701 pages
File Size : 53,8 Mb
Release : 2020-10-08
Category : Mathematics
ISBN : 9789811214837

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Lectures On The Geometry Of Manifolds (Third Edition) by Liviu I Nicolaescu Pdf

The goal of this book is to introduce the reader to some of the main techniques, ideas and concepts frequently used in modern geometry. It starts from scratch and it covers basic topics such as differential and integral calculus on manifolds, connections on vector bundles and their curvatures, basic Riemannian geometry, calculus of variations, DeRham cohomology, integral geometry (tube and Crofton formulas), characteristic classes, elliptic equations on manifolds and Dirac operators. The new edition contains a new chapter on spectral geometry presenting recent results which appear here for the first time in printed form.

Author : Ana Cannas da Silva
Publisher : Springer
Page : 220 pages
File Size : 50,8 Mb
Release : 2004-10-27
Category : Mathematics
ISBN : 9783540453307

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Lectures on Symplectic Geometry by Ana Cannas da Silva Pdf

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.

Author : Tohru Eguchi,Yakov Eliashberg,Yoshiaki Maeda,Mathematical Sciences Research Institute (Berkeley, Calif.)
Publisher : Cambridge University Press
Page : 303 pages
File Size : 51,6 Mb
Release : 2014-08-25
Category : Mathematics
ISBN : 9781107056411

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Symplectic, Poisson, and Noncommutative Geometry by Tohru Eguchi,Yakov Eliashberg,Yoshiaki Maeda,Mathematical Sciences Research Institute (Berkeley, Calif.) Pdf

Consists of refereed papers from two joint workshops held at MSRI in May, 2010.

Author : Mikhail Vladimirovich Karasev,Elena M. Novikova,Yurii Mikhailovich Vorobjev
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 51,8 Mb
Release : 2005
Category : Computers
ISBN : 0821840401

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Quantum Algebras and Poisson Geometry in Mathematical Physics by Mikhail Vladimirovich Karasev,Elena M. Novikova,Yurii Mikhailovich Vorobjev Pdf

Presents applications of Poisson geometry to some fundamental well-known problems in mathematical physics. This volume is suitable for graduate students and researchers interested in mathematical physics. It uses methods such as: unexpected algebras with non-Lie commutation relations, dynamical systems theory, and semiclassical asymptotics.

Author : Jerrold E. Marsden,Tudor S. Ratiu
Publisher : Springer Science & Business Media
Page : 654 pages
File Size : 50,7 Mb
Release : 2007-07-03
Category : Mathematics
ISBN : 9780817644192

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The Breadth of Symplectic and Poisson Geometry by Jerrold E. Marsden,Tudor S. Ratiu Pdf

* The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics