xii Contents §19.4. Moore Spaces 424 §19.5. Homotopy Groups of a Smash Product 427 §19.6. Smash Products of Eilenberg-MacLane Spaces 429 §19.7. An Additional Topic and Some Problems 432 Chapter 20. Further Topics 435 §20.1. The Homotopy Category Is Not Complete 435 §20.2. Cone Decompositions with Respect to Moore Spaces 436 §20.3. First p-Torsion Is a Stable Invariant 438 §20.4. Hopf Invariants and Lusternik-Schnirelmann Category 445 §20.5. Infinite Symmetric Products 448 §20.6. Additional Topics, Problems and Projects 452 Part 5. Cohomology and Homology Chapter 21. Cohomology 459 §21.1. Cohomology 459 §21.2. Basic Computations 467 §21.3. The External Cohomology Product 473 §21.4. Cohomology Rings 475 §21.5. Computing Algebra Structures 479 §21.6. Variation of Coefficients 485 §21.7. A Simple unneth Theorem 487 §21.8. The Brown Representability Theorem 489 §21.9. The Singular Extension of Cohomology 494 §21.10. An Additional Topic and Some Problems and Projects 495 Chapter 22. Homology 499 §22.1. Homology Theories 499 §22.2. Examples of Homology Theories 505 §22.3. Exterior Products and the unneth Theorem for Homology 508 §22.4. Coalgebra Structure for Homology 509 §22.5. Relating Homology to Cohomology 510 §22.6. H-Spaces and Hopf Algebras 512 Chapter 23. Cohomology Operations 515 §23.1. Cohomology Operations 516 §23.2. Stable Cohomology Operations 518
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