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020 _a9780817644192
_9978-0-8176-4419-2
024 7 _a10.1007/b138687
_2doi
050 4 _aQA641-670
072 7 _aPBMP
_2bicssc
072 7 _aMAT012030
_2bisacsh
082 0 4 _a516.36
_223
245 1 4 _aThe Breadth of Symplectic and Poisson Geometry
_h[electronic resource] :
_bFestschrift in Honor of Alan Weinstein /
_cedited by Jerrold E. Marsden, Tudor S. Ratiu.
264 1 _aBoston, MA :
_bBirkhäuser Boston,
_c2005.
300 _aXXIII, 654 p. 30 illus.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aProgress in Mathematics ;
_v232
505 0 _aDirac 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.
520 _aOne 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.
650 0 _aMathematics.
650 0 _aTopological groups.
650 0 _aLie groups.
650 0 _aGeometry.
650 0 _aDifferential geometry.
650 0 _aPhysics.
650 1 4 _aMathematics.
650 2 4 _aDifferential Geometry.
650 2 4 _aTopological Groups, Lie Groups.
650 2 4 _aMathematical Methods in Physics.
650 2 4 _aGeometry.
700 1 _aMarsden, Jerrold E.
_eeditor.
700 1 _aRatiu, Tudor S.
_eeditor.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9780817635657
830 0 _aProgress in Mathematics ;
_v232
856 4 0 _uhttp://dx.doi.org/10.1007/b138687
912 _aZDB-2-SMA
950 _aMathematics and Statistics (Springer-11649)
999 _c506040
_d506040