Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity. II

Download or read book Compact Connected Lie Transformation Groups on Spheres with Low Cohomogeneity. II written by Eldar Straume and published by American Mathematical Soc.. This book was released on 1997 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: The cohomogeneity of a transformation group ([italic capitals]G, X) is, by definition, the dimension of its orbit space, [italic]c = dim [italic capitals]X, G. We are concerned with the classification of differentiable compact connected Lie transformation groups on (homology) spheres, with [italic]c [less than or equal to symbol] 2, and the main results are summarized in five theorems, A, B, C, D, and E in part I. This paper is part II of the project, and addresses theorems D and E. D examines the orthogonal model from theorem A and orbit structures, while theorem E addresses the existence of "exotic" [italic capital]G-spheres.