MAT 1344 S

Group actions on manifolds


TR 12:30-2, Room SS 5017A




Course outline:


An introduction to equivariant cohomology, with emphasis on equivariant de Rham theory.
The following topics will be covered:
  1. Actions of Lie groups and Lie algebras,
  2. Orbit type decompositions,
  3. Classifying bundles,
  4. Equivariant cohomology,
  5. Localization formulas.
References:
  1. Ginzburg, Guillemin and Karshon: Moment Maps, Cobordisms, and Hamiltonian Group Actions, AMS 2002.
  2. Guillemin and Sternberg: Supersymmetry and equivariant de Rham theory, Springer 1999.
  3. Kumar and Vergne: Equivariant Cohomology with Generalized Coefficients, Asterisque, 1993 (215), 109-204.
  4. Duistermaat and Kolk: : Lie groups, Springer 2000.
  5. Onishchik, Vinberg and Gorbatsevich: Foundations of Lie Theory and Lie Transformation Groups, Springer 1997.