Contents ix §6.2. Cofibrant Diagrams 146 §6.3. Homotopy Colimits of Diagrams 151 §6.4. Constructing Cofibrant Replacements 155 §6.5. Examples: Pushouts, 3 × 3s and Telescopes 160 §6.6. Homotopy Limits 167 §6.7. Functors Applied to Homotopy Limits and Colimits 173 §6.8. Homotopy Colimits of More General Diagrams 176 §6.9. Additional Topics, Problems and Projects 178 Chapter 7. Homotopy Pushout and Pullback Squares 181 §7.1. Homotopy Pushout Squares 181 §7.2. Recognition and Completion 185 §7.3. Homotopy Pullback Squares 188 §7.4. Manipulating Squares 190 §7.5. Characterizing Homotopy Pushout and Pullback Squares 195 §7.6. Additional Topics, Problems and Projects 196 Chapter 8. Tools and Techniques 199 §8.1. Long Cofiber and Fiber Sequences 199 §8.2. The Action of Paths in Fibrations 203 §8.3. Every Action Has an Equal and Opposite Coaction 205 §8.4. Mayer-Vietoris Sequences 209 §8.5. The Operation of Paths 211 §8.6. Fubini Theorems 212 §8.7. Iterated Fibers and Cofibers 214 §8.8. Group Actions 216 Chapter 9. Topics and Examples 221 §9.1. Homotopy Type of Joins and Products 221 §9.2. H-Spaces and co-H-Spaces 225 §9.3. Unitary Groups and Their Quotients 230 §9.4. Cone Decompositions 237 §9.5. Introduction to Phantom Maps 245 §9.6. G. W. Whitehead’s Homotopy Pullback Square 249 §9.7. Lusternik-Schnirelmann Category 250 §9.8. Additional Problems and Projects 258
Previous Page Next Page