Table of Contents Introduction 1 Chapter I : Linear groups of cohomogeneity 4 7 Chapter II : Determination of weight patterns 15 §1 : A review of the geometric weight system and some basic techniques 15 §2 : Actions of small groups 2 2 §3 : Actions of simple groups 3 6 §4 : Analysis of weight patterns in general 4 8 Chapter III :Fixed point results of P.A.Smith type 7 1 Chapter IV : Classification of compact connected Lie transformation groups on spheres with cohomogeneity one 7 5 §1: Basic facts and constructions 7 5 §2 : G-spheres of cohomogeneity one. Proof of Theorem C 7 7 Appendix : Table I, II, III c(D) 3 82 References 91 V
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