Introduction To Compact Transformation Groups

Introduction to Compact Transformation Groups

In this book, the author carries out a systematic investigation and construction of all possible differentiable (homotopy) G-spheres with 2-dimensional orbit space, where G is any compact connected Lie group. Based on the geometric weight system classification of Part I, the possible orbit structures are determined, and the exotic G-spheres are constructed by equivariant twisting of the orthogonal models.

This text is aimed at researchers studying Lie 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.