Calculus of smooth mappings Calculus of holomorphic and real analytic mappings Partitions of unity Smoothly realcompact spaces Extensions and liftings of mappings Infinite dimensional manifolds Calculus on infinite dimensional manifolds Infinite dimensional differential geometry Manifolds of mappings Further applications
Providence, R.I. : American Mathematical Society, [2008]
9780821820032 (alkaline paper)
Differentiable manifolds -- Submersions and immersions -- Vector fields and flows -- Lie groups I -- Lie groups II. Lie subgroups and homogeneous spaces -- Transformation groups and g-manifolds -- Polynomial and smooth invariant theory -- Vector bundles -- Differential forms -- Integration on manifolds -- De Rham cohomology -- Cohomology with compact supports and Poincaré duality -- De Rham cohomology of compact manifolds -- Lie groups III. Analysis on Lie groups -- Extensions of Lie algebras and Lie groups -- Derivations on the Algebra of Differential Forms -- Fiber Bundles and Connections -- Principal Fiber Bundles and G-Bundles -- Principal and Induced Connections -- Characteristic classes -- Jets -- Pseudo Riemann metrics and the Levi Civita covariant derivative -- Riemann geometry of geodesics -- Parallel transport and curvature -- Computing with adapted frames, and examples -- Riemann immersions and submersions -- Jacobi fields -- Isometries, homogeneous manifolds, and symmetric spaces -- Riemann G-manifolds -- Polar actions -- Symplectic geometry and classical mechanics -- Completely integrable Hamiltonian systems -- Poisson manifolds -- Hamiltonian group actions and momentum mappings.
