Momentum Maps and Hamiltonian Reduction

The use of symmetries and conservation laws in the qualitative description of dynamics has a long history going back to the founders of classical mechanics. The focus of this work is a comprehensive and self-contained presentation of the intimate connection between symmetries, conservation laws, and reduction, treating the singular case in detail. This Ferran Sunyer i Balaguer Prize-winning monograph is the first self-contained and thorough presentation of the theory of Hamiltonian reduction in the presence of singularities. It can serve as a resource for graduate courses and seminars in symplectic and Poisson geometry, mechanics, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers.

Winner of the Ferran Sunyer i Balaguer Prize in 2000 Reviews the necessary prerequisites, beginning with an introduction to Lie symmetries on Poisson and symplectic manifolds Currently in classroom use in Europe Can serve as a resource for graduate courses and seminars in Hamiltonian mechanics and symmetry, symplectic and Poisson geometry, Lie theory, mathematical physics, and as a comprehensive reference resource for researchers

Inhalt
1 Manifolds and Smooth Structures.- 2 Lie Group Actions.- 3 Pseudogroups and Groupoids.- 4 The Standard Momentum Map.- 5 Generalizations of the Momentum Map.- 6 Regular Symplectic Reduction Theory.- 7 The Symplectic Slice Theorem.- 8 Singular Reduction and the Stratification Theorem.- 9 Optimal Reduction.- 10 Poisson Reduction.- 11 Dual Pairs.