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 $\lt 3$.
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.
