Lectures On Poisson Geometry
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Author | : Marius Crainic |
Publisher | : American Mathematical Soc. |
Total Pages | : 479 |
Release | : 2021-10-14 |
Genre | : Education |
ISBN | : 1470466678 |
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 | : Giuseppe Dito |
Publisher | : American Mathematical Soc. |
Total Pages | : 330 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 0821844237 |
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 | : Izu Vaisman |
Publisher | : Birkhäuser |
Total Pages | : 210 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3034884958 |
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 | : Izu Vaisman |
Publisher | : Springer Science & Business Media |
Total Pages | : 222 |
Release | : 1994-03-01 |
Genre | : Mathematics |
ISBN | : 9783764350161 |
Everybody having even the slightest interest in analytical mechanics remembers having met there the Poisson bracket of two functions of 2n variables (pi, qi) f g (8f8g 8 8 ) (0.1) {f, g} = L... [ji - [ji; =1 p, q q p, and the fundamental role it plays in that field. In modern works, this bracket is derived from a symplectic structure, and it appears as one of the main in- gredients of symplectic manifolds. In fact, it can even be taken as the defining clement of the structure (e.g., [TIl]). But, the study of some mechanical sys- tems, particularly systems with symmetry groups or constraints, may lead to more general Poisson brackets. Therefore, it was natural to define a mathematical structure where the notion of a Poisson bracket would be the primary notion of the theory, and, from this viewpoint, such a theory has been developed since the early 19708, by A. Lichnerowicz, A. Weinstein, and many other authors (see the references at the end of the book). But, it has been remarked by Weinstein [We3] that, in fact, the theory can be traced back to S. Lie himself [Lie].
Author | : Marius Crainic |
Publisher | : |
Total Pages | : |
Release | : 1900 |
Genre | : Electronic books |
ISBN | : 9781470466664 |
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 | : Günter Last |
Publisher | : Cambridge University Press |
Total Pages | : 315 |
Release | : 2017-10-26 |
Genre | : Mathematics |
ISBN | : 1107088011 |
A modern introduction to the Poisson process, with general point processes and random measures, and applications to stochastic geometry.
Author | : |
Publisher | : |
Total Pages | : 0 |
Release | : 2011 |
Genre | : Poisson manifolds |
ISBN | : |
Author | : Günter Last |
Publisher | : Cambridge University Press |
Total Pages | : 316 |
Release | : 2017-10-26 |
Genre | : Mathematics |
ISBN | : 1108514901 |
The Poisson process, a core object in modern probability, enjoys a richer theory than is sometimes appreciated. This volume develops the theory in the setting of a general abstract measure space, establishing basic results and properties as well as certain advanced topics in the stochastic analysis of the Poisson process. Also discussed are applications and related topics in stochastic geometry, including stationary point processes, the Boolean model, the Gilbert graph, stable allocations, and hyperplane processes. Comprehensive, rigorous, and self-contained, this text is ideal for graduate courses or for self-study, with a substantial number of exercises for each chapter. Mathematical prerequisites, mainly a sound knowledge of measure-theoretic probability, are kept in the background, but are reviewed comprehensively in the appendix. The authors are well-known researchers in probability theory; especially stochastic geometry. Their approach is informed both by their research and by their extensive experience in teaching at undergraduate and graduate levels.
Author | : Sebastián Montiel |
Publisher | : American Mathematical Soc. |
Total Pages | : 395 |
Release | : 2009 |
Genre | : Mathematics |
ISBN | : 0821847635 |
Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.
Author | : Izu Vaisman |
Publisher | : |
Total Pages | : 96 |
Release | : 2000 |
Genre | : Differentiable manifolds |
ISBN | : |