Spaces of PL Manifolds and Categories of Simple Maps

Introduction 1
1. The stable parametrized h-cobordism theorem 7
1.1. The manifold part 7
1.2. The non-manifold part 13
1.3. Algebraic K-theory of spaces 15
1.4. Relation to other literature 20
2. On simple maps 29
2.1. Simple maps of simplicial sets 29
2.2. Normal subdivision of simplicial sets 34
2.3. Geometric realization and subdivision 42
2.4. The reduced mapping cylinder 56
2.5. Making simplicial sets non-singular 68
2.6. The approximate lifting property 74
2.7. Subdivision of simplicial sets over Δ^q 83
3. The non-manifold part 99
3.1. Categories of simple maps 99
3.2. Filling horns 108
3.3. Some homotopy fiber sequences 119
3.4. Polyhedral realization 126
3.5. Turning Serre fibrations into bundles 131
3.6. Quillen's Theorems A and B 134
4. The manifold part 139
4.1. Spaces of PL manifolds 139
4.2. Spaces of thickenings 150
4.3. Straightening the thickenings 155
Bibliography 175
Symbols 179
Index 181