Contents Preface xiii Chapter 1. Transformation Groups 1 1.1. Introduction 1 1.2. (Locally) Proper G-spaces 4 1.3. Fiber bundles 6 1.4. Classifying spaces 9 1.5. Borel spaces and classifying spaces 10 1.6. Tubular neighborhoods and slices 11 1.7. Existence of slices 15 1.8. Cohomology manifolds and the Smith theorems 18 1.9. Actions of G·Π (G Lie group, Π discrete) 20 Chapter 2. Group Actions and the Fundamental Group 23 2.1. Covering spaces 23 2.2. Lifting group actions to covering spaces 26 2.3. Lifting an action of G when G has a fixed point 28 2.4. Evaluation homomorphism 31 2.5. Lifting connected group actions 32 2.6. Example (Semi-free S1-actions on 3-manifolds) 35 2.7. Lifting the slice representation 39 2.8. Locally injective actions 42 Chapter 3. Actions of Compact Lie Groups on Manifolds 47 3.1. Actions of compact Lie groups on aspherical manifolds 47 3.2. Actions of compact Lie groups on admissible manifolds 54 3.3. Compact Lie group actions on spaces which map into K(Γ, 1) 59 3.4. Manifolds with few or no periodic homeomorphisms 65 3.5. Injective torus actions 66 Chapter 4. Definition of Seifert Fibering 69 4.1. Examples 69 4.2. TOPG(P), the group of weak G-equivalences 73 4.3. Seifert fiberings modeled on a principal G-bundle 78 4.4. The topology and geometry of the fibers 81 4.5. Examples with Π discrete 83 4.6. The Seifert Construction 91 Chapter 5. Group Cohomology 95 5.1. Introduction 95 5.2. Group extensions 95 ix
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