Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I

Download or read book Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity, I written by Eldar Straume and published by American Mathematical Soc.. This book was released on 1996-02-05 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the study of Lie transformation groups on classical space forms, one of the most exciting features is the existence of nonlinear or ``exotic'' actions. Among the many unsolved problems, the classification of G-spheres with 2-dimensional orbit space has a prominent place. The main purpose of this monograph is to describe the beginnings of a program to the complete solution of this problem. One major feature of the author's approach is the effectiveness of the geometric weight system, which was introduced by Wu-Yi Hsiang around 1970, as a book-keeping method for orbit structural data. Features: Complete tables of compact connected linear groups of cohomogeneity $< 3$. Geometric weight systems techniques. Complete classification of G-spheres of cohomogeneity one. Weight classification of G-spheres of cohomogeneity two, the crucial step of the complete classification for cohomogeneity two.