Abstract
Introduction .220 Chapter I. A fixed point theorem for finite diffeomorphism groups generated by reflections 221 Chapter II. Geometric weight system and a fixed point theorem for compact connected Lie groups.... 231 1. Actions of compact simple Lie groups of rank 1.232 2. Basic properties of the geometric weight system.237 3. A fixed point theorem for compact connected Lie groups.240 Chapter III. Classification of the types of principal isotropy subgroups for actions of compact connected Lie groups on acyclic manifolds .242 1. Classification of principal orbit types for actions of simple compact connected Lie groups on acyclic manifolds .243 2. Classification of principal orbit types for actions of general compact connected Lie groups .247 References ...... 255
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