The Breadth Of Symplectic And Poisson Geometry

by Marsden, Jerrold E.; Ratiu, Tudor S.; Weinstein, Alan

• ISBN13: 9780817635657
• ISBN10: 0817635653
• Format: Hardcover
• Copyright: 2004-11-01
• Publisher: Birkhauser

Summary

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.Intended for graduate students and working mathematicians in symplectic and Poisson geometry as well as mechanics, this text is a distillation of prominent research and an indication of the future trends and directions in geometry, mechanics, and mathematical physics.Contributors: H. Bursztyn, M. Cahen, M. Crainic, J. J. Duistermaat, K. Ehlers, S. Evens, V. L. Ginzburg, A. B. Givental, S. Gutt, D. D. Holm, J. Huebschmann, L. Jeffrey, F. Kirwan, M. Kogan, J. Koiller, Y. Kosmann-Schwarzbach, B. Kostant, C. Laurent-Gengoux, J-H. Lu, J. E. Marsden, K. C. H. Mackenzie, Y. Maeda, C-M. Marle, T. E. Milanov, N. Miyazaki, R. Montgomery, Y-G. Oh, J-P. Ortega, H. Omori, T. S. Ratiu, P. M. Rios, L. Schwachhöfer, J. Stasheff, I. Vaisman, A. Yoshioka, P. Xu, and S. Zelditch.

Table of Contents

Preface	ix
Academic genealogy of Alan Weinstein	xiii
About Alan Weinstein	xv
Students of Alan Weinstein	xv
Alan Weinstein's publications	xvi
Dirac structures, momentum maps, and quasi-Poisson manifolds
Henrique Bursztyu, Marius Crainic	1	(40)
Construction of Ricci-type connections by reduction and induction
Michel Callen, Simone Gutt, Lorenz Schwachhöfer	41	(18)
A mathematical model for geomagnetic reversals
J.J. Duistermaat	59	(16)
Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization
Kurt Ehlers, Jair Koiller, Richard Montgomery, Pedro M. Rios	75	(46)
Thompson's conjecture for real semisimple Lie groups
Sam Evens, Jiang-Hua Lu	121	(18)
The Weinstein conjecture and theorems of nearby and almost existence
Viktor L. Ginzburg	139	(34)
Simple singularities and integrable hierarchies
Alexander B. Givental, Todor E. Milanov	173	(30)
Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation
Darryl D. Holm, Jerrold E. Marsden	203	(34)
Higher homotopies and Maurer-Cartan algebras: Quasi-Lie-Rinehart, Gerstenhaber, and Batalin-Vilkovisky algebras
Johannes Huebschmann	237	(66)
Localization theorems by symplectic cuts
Lisa Jeffrey, Mikhail Kogan	303	(24)
Refinements of the Morse stratification of the normsquare of the moment map
Frances Kirwan	327	(36)
Quasi, twisted, and all that...in Poisson geometry and Lie algebroid theory
Yvette Kosmann-Schwarzbach	363	(28)
Minimal coadjoint orbits and symplectic induction
Bertram Kostant	391	(32)
Quantization of pre-quasi-symplectic groupoids and their Hamiltonian spaces
Camille Laurent-Gengoux, Ping Xu	423	(32)
Duality and triple structures
Kirill C.H. Mackenzie	455	(28)
Star exponential functions as two-valued elements
Y. Maeda, N. Miyazaki, H. Omori, A. Yoshioka	483	(10)
From momentum maps and dual pairs to symplectic and Poisson groupoids
Charles-Michel Made	493	(32)
Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds
Yong-Geun Oh	525	(46)
The universal covering and covered spaces of a symplectic Lie algebra action
Juan-Pablo Ortega, Tudor S. Ratiu	571	(12)
Poisson homotopy algebra: An idiosyncratic survey of homotopy algebraic topics related to Alan's interests
Jim Stasheff	583	(20)
Dirac submanifolds of Jacobi manifolds
Izu Vaisman	603	(20)
Quantum maps and automorphisms
Steve Zelditch	623