Current Trends in Transformation Groups [Paperback]

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.

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.

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 comló-