Contents xi §15.4. Some Theory of Fiber Bundles 333 §15.5. Serre Fibrations and Model Structures 336 §15.6. The Simplicial Approach to Homotopy Theory 341 §15.7. Quasifibrations 346 §15.8. Additional Problems and Projects 348 Part 4. Targets as Domains, Domains as Targets Chapter 16. Constructions of Spaces and Maps 353 §16.1. Skeleta of Spaces 354 §16.2. Connectivity and CW Structure 357 §16.3. Basic Obstruction Theory 359 §16.4. Postnikov Sections 361 §16.5. Classifying Spaces and Universal Bundles 363 §16.6. Additional Problems and Projects 371 Chapter 17. Understanding Suspension 373 §17.1. Moore Paths and Loops 373 §17.2. The Free Monoid on a Topological Space 376 §17.3. Identifying the Suspension Map 379 §17.4. The Freudenthal Suspension Theorem 382 §17.5. Homotopy Groups of Spheres and Wedges of Spheres 383 §17.6. Eilenberg-MacLane Spaces 384 §17.7. Suspension in Dimension 1 387 §17.8. Additional Topics and Problems 389 Chapter 18. Comparing Pushouts and Pullbacks 393 §18.1. Pullbacks and Pushouts 393 §18.2. Comparing the Fiber of f to Its Cofiber 396 §18.3. The Blakers-Massey Theorem 398 §18.4. The Delooping of Maps 402 §18.5. The n-Dimensional Blakers-Massey Theorem 405 §18.6. Additional Topics, Problems and Projects 409 Chapter 19. Some Computations in Homotopy Theory 413 §19.1. The Degree of a Map Sn Sn 414 §19.2. Some Applications of Degree 417 §19.3. Maps Between Wedges of Spheres 421
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