Contents Preface ix Chapter 1. Introduction 1 1.1. Motivation 1 1.2. The main theorems for Haken 3-manifolds 3 1.3. The main theorems for reducible 3-manifolds 8 1.4. Examples 9 Chapter 2. Johannson's Characteristic Submanifold Theory 15 2.1. Fibered 3-manifolds 16 2.2. Boundary patterns 20 2.3. Admissible maps and mapping class groups 23 2.4. Essential maps and useful boundary patterns 28 2.5. The classical theorems 35 2.6. Exceptional fibered 3-manifolds 38 2.7. Vertical and horizontal surfaces and maps 40 2.8. Fiber-preserving maps 41 2.9. The characteristic submanifold 48 2.10. Examples of characteristic submanifolds 51 2.11. The Classification Theorem 57 2.12. Miscellaneous topological results 60 Chapter 3. Relative Compression Bodies and Cores 65 3.1. Relative compression bodies 66 3.2. Minimally imbedded relative compression bodies 69 3.3. The maximal incompressible core 71 3.4. Normally imbedded relative compression bodies 73 3.5. The normal core and the useful core 74 Chapter 4. Homotopy Types 77 4.1. Homotopy equivalences preserve usefulness 77 4.2. Finiteness of homotopy types 83 Chapter 5. Pared 3-Manifolds 87 5.1. Definitions and basic properties 87 5.2. The topology of pared manifolds 89 5.3. The characteristic submanifold of a pared manifold 92 Chapter 6. Small 3-Manifolds 97 6.1. Small manifolds and small pared manifolds 97 6.2. Small pared homotopy types 101
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