Breadth of Symplectic and Poisson Geometry

• 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.

"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 Mathematiques Pures et Appliquees