Proper Actions and Representation Theory

Introduction. 1. Hilbert's fifth problem and proper actions of Lie groups S. Illman. 2. Equivariant algebraic vector bundles over representations - a survey M. Masuda. 3. G-manifolds and G-vector bundles in algebraic, semialgebraic, and definable categories T. Kawakami. 4. Geometry of Finite Topological and equivariant finite topological spaces S. Kono, F. Ushitaki. 5. On the theory of homotopy representations. A survey I. Nagasaki. 6. Manifolds as fixed point sets of smooth compact Lie group actions K. Pawalowski. 7. Surgery and homotopy theory in study of the transformation groups Y. Kitada. 8. Kervaire's obstructions of free actions of finite cyclic groups on homotopy spheres Y. Kitada. 9. The Burnside ring revisited M. Morimoto. 10. Multiplicative stabilization and transformation groups S. Kwasik, R. Schultz. 11. Symmetries on manifolds, deformations and rational homotopy: a survey M. Raussen. 12. Rigidity of codimension one locally free actions of solvable Lie groups N. Tsuchiya, A. Yamakawa. 13. Smooth actions of non-compact semi-simple Lie groups F. Uchida, K. Mukoyama. 14. Hamiltonian group actions and equivariant indices T. Takakura. 15. Controlled methods in equivariant topology, a survey E. Pedersen. Index.

Involutions and representations for reduced quantum algebras