One of the world's foremost geometers, Alan Weinstein has made deep contributions to symplectic and differential geometry, Lie theory, mechanics, and related fields. Contributors to this text in Weinstein's honor 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.
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.
Inhalt
Dirac structures, momentum maps, and quasi-Poisson manifolds.- Construction of Ricci-type connections by reduction and induction.- A mathematical model for geomagnetic reversals.- Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization.- Thompson's conjecture for real semisimple Lie groups.- The Weinstein conjecture and theorems of nearby and almost existence.- Simple singularities and integrable hierarchies.- Momentum maps and measure-valued solutions (peakons, filaments, and sheets) for the EPDiff equation.- Higher homotopies and Maurer-Cartan algebras: Quasi-Lie-Rinehart, Gerstenhaber, and Batalin-Vilkovisky algebras.- Localization theorems by symplectic cuts.- Refinements of the Morse stratification of the normsquare of the moment map.- Quasi, twisted, and all that... in Poisson geometry and Lie algebroid theory.- Minimal coadjoint orbits and symplectic induction.- Quantization of pre-quasi-symplectic groupoids and their Hamiltonian spaces.- Duality and triple structures.- Star exponential functions as two-valued elements.- From momentum maps and dual pairs to symplectic and Poisson groupoids.- Construction of spectral invariants of Hamiltonian paths on closed symplectic manifolds.- The universal covering and covered spaces of a symplectic Lie algebra action.- Poisson homotopy algebra: An idiosyncratic survey of homotopy algebraic topics related to Alan's interests.- Dirac submanifolds of Jacobi manifolds.- Quantum maps and automorphisms.