Memoirs of the American Mathematical Society 1996; 93 pp; softcover Volume: 119 ISBN10: 082180409X ISBN13: 9780821804094 List Price: US$41 Individual Members: US$24.60 Institutional Members: US$32.80 Order Code: MEMO/119/569
 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 Gspheres with 2dimensional 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 WuYi Hsiang around 1970, as a bookkeeping method for orbit structural data. Features:  Complete tables of compact connected linear groups of cohomogeneity \(< 3\).
 Geometric weight systems techniques.
 Complete classification of Gspheres of cohomogeneity one.
 Weight classification of Gspheres of cohomogeneity two, the crucial step of the complete classification for cohomogeneity two.
Readership Graduate students and research mathematicians in topology/geometry, invariant theory, theoretical physics and physicists who apply Lie theory. Table of Contents  Introduction
 Linear groups of cohomogeneity \(< 4\)
 Determination of weight patterns
 Fixed point results of P. A. Smith type
 Classification of compact connected Lie transformation
 Appendix
 References
