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Birkhäuser

The Breadth of Symplectic and Poisson Geometry

Festschrift in Honor of Alan Weinstein

  • Book
  • © 2005

Overview

Editors:
  1. Jerrold E. Marsden

    1. Department of Engineering and Applied Science Control and Dynamical Systems, California Institute of Technology, Pasadena, USA

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  2. Tudor S. Ratiu

    1. Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

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  • 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

Part of the book series: Progress in Mathematics (PM, volume 232)

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Table of contents (22 chapters)

  1. Front Matter

    Pages i-xxiii
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  2. Dirac structures, momentum maps, and quasi-Poisson manifolds

    • Henrique Bursztyn, Marius Crainic
    Pages 1-40

  3. Construction of Ricci-type connections by reduction and induction

    • Michel Cahen, Simone Gutt, Lorenz Schwachhöfer
    Pages 41-57

  4. A mathematical model for geomagnetic reversals

    • J. J. Duistermaat
    Pages 59-73

  5. Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization

    • Kurt Ehlers, Jair Koiller, Richard Montgomery, Pedro M. Rios
    Pages 75-120

  6. Thompson’s conjecture for real semisimple Lie groups

    • Sam Evens, Jiang-Hua Lu
    Pages 121-137

  7. The Weinstein conjecture and theorems of nearby and almost existence

    • Viktor L. Ginzburg
    Pages 139-172

  8. Simple singularities and integrable hierarchies

    • Alexander B. Givental, Todor E. Milanov
    Pages 173-201

  9. Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation

    • Darryl D. Holm, Jerrold E. Marsden
    Pages 203-235

  10. Higher homotopies and Maurer-Cartan algebras: Quasi-Lie-Rinehart, Gerstenhaber, and Batalin-Vilkovisky algebras

    • Johannes Huebschmann
    Pages 237-302

  11. Localization theorems by symplectic cuts

    • Lisa Jeffrey, Mikhail Kogan
    Pages 303-326

  12. Refinements of the Morse stratification of the normsquare of the moment map

    • Frances Kirwan
    Pages 327-362

  13. Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory

    • Yvette Kosmann-Schwarzbach
    Pages 363-389

  14. Minimal coadjoint orbits and symplectic induction

    • Bertram Kostant
    Pages 391-422

  15. Quantization of pre-quasi-symplectic groupoids and their Hamiltonian spaces

    • Camille Laurent-Gengoux, Ping Xu
    Pages 423-454

  16. Duality and triple structures

    • Kirill C. H. Mackenzie
    Pages 455-481

  17. Star exponential functions as two-valued elements

    • Y. Maeda, N. Miyazaki, H. Omori, A. Yoshioka
    Pages 483-492

  18. From momentum maps and dual pairs to symplectic and Poisson groupoids

    • Charles-Michel Marle
    Pages 493-523

  19. Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds

    • Yong-Geun Oh
    Pages 525-570

  20. The universal covering and covered spaces of a symplectic Lie algebra action

    • Juan-Pablo Ortega, Tudor S. Ratiu
    Pages 571-581
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Keywords

About this book

One of the world’s foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields. Written in his honor, the invited papers in this volume reflect the active and vibrant research in these areas and are a tribute to Weinstein’s ongoing influence.

The well-recognized contributors to this text cover a broad range of topics: Induction and reduction for systems with symmetry, symplectic geometry and topology, geometric quantization, the Weinstein Conjecture, Poisson algebra and geometry, Dirac structures, deformations for Lie group actions, Kähler geometry of moduli spaces, theory and applications of Lagrangian and Hamiltonian mechanics and dynamics, symplectic and Poisson groupoids, and quantum representations.

Reviews

"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

Editors and Affiliations

  • Department of Engineering and Applied Science Control and Dynamical Systems, California Institute of Technology, Pasadena, USA

    Jerrold E. Marsden

  • Département de Mathématiques, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland

    Tudor S. Ratiu

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