Contents xiii §23.3. Using the Diagonal Map to Construct Cohomology Operations 521 §23.4. The Steenrod Reduced Powers 525 §23.5. The ´ Adem Relations 528 §23.6. The Algebra of the Steenrod Algebra 533 §23.7. Wrap-Up 538 Chapter 24. Chain Complexes 541 §24.1. The Cellular Complex 542 §24.2. Applying Algebraic Universal Coefficients Theorems 547 §24.3. The General K¨ unneth Theorem 548 §24.4. Algebra Structures on C∗(X) and C∗(X) 550 §24.5. The Singular Chain Complex 551 Chapter 25. Topics, Problems and Projects 553 §25.1. Algebra Structures on Rn and Cn 553 §25.2. Relative Cup Products 554 §25.3. Hopf Invariants and Hopf Maps 556 §25.4. Some Homotopy Groups of Spheres 563 §25.5. The Borsuk-Ulam Theorem 565 §25.6. Moore Spaces and Homology Decompositions 567 §25.7. Finite Generation of π∗(X) and H∗(X) 570 §25.8. Surfaces 572 §25.9. Euler Characteristic 573 §25.10. The K¨ unneth Theorem via Symmetric Products 576 §25.11. The Homology Algebra of ΩΣX 576 §25.12. The Adjoint λX of idΩX 577 §25.13. Some Algebraic Topology of Fibrations 579 §25.14. A Glimpse of Spectra 580 §25.15. A Variety of Topics 581 §25.16. Additional Problems and Projects 585 Part 6. Cohomology, Homology and Fibrations Chapter 26. The Wang Sequence 591 §26.1. Trivialization of Fibrations 591 §26.2. Orientable Fibrations 592 §26.3. The Wang Cofiber Sequence 593
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