Current Trends in Transformation Groups

This book provides an overview of some of the most active topics in the theory of transformation groups over the past decades and stresses advances obtained in the last dozen years. The emphasis is on actions of Lie groups on manifolds and CW complexes. Manifolds and actions of Lie groups on them are studied in the linear, semialgebraic, definable, analytic, smooth, and topological categories. Equivalent vector bundles play an important role.

The work is divided into fifteen articles and will be of interest to anyone researching or studying transformations groups. The references make it easy to find details and original accounts of the topics surveyed, including tools and theories used in these accounts.

Auteur
Masaharu Morimoto begann seine Kochkarriere in Hiroshima mit einer achtjährigen Ausbildung in einem Sushirestaurant. Schon mit 24 Jahren eröffnete er sein erstes eigenes Restaurant. Mit seinem innovativen Mix aus japanischer Tradition, westlichen Kochtechniken und europäischen Zutaten erwarb er sich bald den Ruf als Erneuerer der japanischen Küche. Nach fünf Jahren verließ Morimoto Japan und machte sich daran, die USA zu erobern - was ihm eindrucksvoll gelang: Heute besitzt er mehrere Restaurants in New York, Philadelphia und Tokio sowie eine eigene Sake und Bierbrauerei.

Contenu

1. Hilbert's fifth problem and proper actions of Lie groups.- 2. Equivariant algebraic vector bundles over representations a survey.- 3. G-manifolds and G-vector bundles in algebraic, semialgebraic, and definable categories.- 4. Geometry of Finite Topological spaces and equivariant finite topological spaces.- 5. On the theory of homotopy representations. A survey.- 6. Manifolds as fixed point sets of smooth compact Lie group actions.- 7. Surgery and homotopy theory in study of the transformation groups.- 8. Kervaire's obstructions of free actions of finite cyclic groups on homotopy spheres.- 9. The Burnside ring revisited.- 10. Multiplicative stabilization and transformation groups.- 11. Symmetries on manifolds, deformations and rational homotopy: a survey.- 12. Rigidity of codimension one locally free actions of solvable Lie groups.- 13. Smooth actions of non-compact semi-simple Lie groups.- 14. Hamiltonian group actions ana equivariant indices.- 15. Controlled methods in equivariant topology, a survey.