The Breadth of Symplectic and Poisson Geometry
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"This volume will certainly be useful to a broad audience including people interested in fields such as differential geometry, mechanics, differential equations and Lie theory." ---Revue Roumaine de Mathématiques Pures et Appliquées
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This paper builds on three ideas pursued by Alan Weinstein in some of his many fundamental contributions to Poisson geometry: First, Lie algebroids play a prominent role in the study of Poisson manifolds [8, 30]; second, Poisson maps can be regarded as generalized momentum maps for actions of symplectic groupoids [25, 31]; third, Poisson structures on manifolds are particular examples of more general objects called Dirac structures [12, 13, 28]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
compatible prequantization, star exponential functions, descendent potential, trivial cobracket, moment map condition, symplectic induction, normalized submanifold, bigraded bracket, symplectic cut, symplectic groupoid, presymplectic realization, unperturbed deterministic system, deriving operator, algebroid structure, nonholonomic geodesics, semistable points, submanifold iff, nonholonomic geometry, nonholonomic structure, algebroid theory, algebroid action, intertwiner spaces, peakon solutions, groupoïdes symplectiques, stratum indexed Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Alan Weinstein, Poisson Lie, Boutet de Monvel, American Mathematical Society, Differential Geom, Functional Anal, Cambridge University Press, Duke Math, Paris Sér, Hamiltonian F-space, Toeplitz Fourier, Hamiltonian G-spaces, Pure Appl, Contemporary Mathematics, Hamiltonian Poisson, Hamiltonian Seifert, Regular Chaotic Dynam, Reine Angew, University of California, Academic Press, Erwin Schrödinger Institute, Kluwer Academic Publishers, Mathematical Sciences Research Institute Publications, Novikov Floer New!
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This paper builds on three ideas pursued by Alan Weinstein in some of his many fundamental contributions to Poisson geometry: First, Lie algebroids play a prominent role in the study of Poisson manifolds [8, 30]; second, Poisson maps can be regarded as generalized momentum maps for actions of symplectic groupoids [25, 31]; third, Poisson structures on manifolds are particular examples of more general objects called Dirac structures [12, 13, 28]. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
compatible prequantization, star exponential functions, descendent potential, trivial cobracket, moment map condition, symplectic induction, normalized submanifold, bigraded bracket, symplectic cut, symplectic groupoid, presymplectic realization, unperturbed deterministic system, deriving operator, algebroid structure, nonholonomic geodesics, semistable points, submanifold iff, nonholonomic geometry, nonholonomic structure, algebroid theory, algebroid action, intertwiner spaces, peakon solutions, groupoïdes symplectiques, stratum indexed Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Alan Weinstein, Poisson Lie, Boutet de Monvel, American Mathematical Society, Differential Geom, Functional Anal, Cambridge University Press, Duke Math, Paris Sér, Hamiltonian F-space, Toeplitz Fourier, Hamiltonian G-spaces, Pure Appl, Contemporary Mathematics, Hamiltonian Poisson, Hamiltonian Seifert, Regular Chaotic Dynam, Reine Angew, University of California, Academic Press, Erwin Schrödinger Institute, Kluwer Academic Publishers, Mathematical Sciences Research Institute Publications, Novikov Floer New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 83
books:
See all 83 books this book cites
3
books
cite this book:
- Floer Memorial Volume (Progress in Mathematics) by Helmut Hofer on 4 pages
- Symplectic Geometry (London Mathematical Society Lecture Note Series) by Dietmar Salamon on page 168, page 171, and page 570
- The Geometry of the Group of Symplectic Diffeomorphism (Lectures in Mathematics. ETH Zürich) by Leonid Polterovich on page 171, and page 570
- Symplectic Geometry and Mathematical Physics (Progress in Mathematics) (French Edition) by P. Donato in Front Matter, and page 300
- Algebraic Topology by Edwin H. Spanier on page 454, and page 581
See all 83 books this book cites
- Lie Theory: Unitary Representations and Compactifications of Symmetric Spaces (Progress in Mathematics) by Jean-Philippe Anker in Back Matter
- Frobenius Splitting Methods in Geometry and Representation Theory (Progress in Mathematics) by Michel Brion in Back Matter
- Geometric Methods in Algebra and Number Theory (Progress in Mathematics) by Fedor Bogomolov on page
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