xiv Contents §26.4. Some Algebraic Topology of Unitary Groups 597 §26.5. The Serre Filtration 600 §26.6. Additional Topics, Problems and Projects 603 Chapter 27. Cohomology of Filtered Spaces 605 §27.1. Filtered Spaces and Filtered Groups 606 §27.2. Cohomology and Cone Filtrations 612 §27.3. Approximations for General Filtered Spaces 615 §27.4. Products in E∗,∗(X) 1 618 §27.5. Pointed and Unpointed Filtered Spaces 620 §27.6. The Homology of Filtered Spaces 620 §27.7. Additional Projects 621 Chapter 28. The Serre Filtration of a Fibration 623 §28.1. Identification of E2 for the Serre Filtration 623 §28.2. Proof of Theorem 28.1 625 §28.3. External and Internal Products 631 §28.4. Homology and the Serre Filtration 633 §28.5. Additional Problems 633 Chapter 29. Application: Incompressibility 635 §29.1. Homology of Eilenberg-MacLane Spaces 636 §29.2. Reduction to Theorem 29.1 636 §29.3. Proof of Theorem 29.2 638 §29.4. Consequences of Theorem 29.1 641 §29.5. Additional Problems and Projects 642 Chapter 30. The Spectral Sequence of a Filtered Space 645 §30.1. Approximating Grs Hn(X) by Er s,n (X) 646 §30.2. Some Algebra of Spectral Sequences 651 §30.3. The Spectral Sequences of Filtered Spaces 654 Chapter 31. The Leray-Serre Spectral Sequence 659 §31.1. The Leray-Serre Spectral Sequence 659 §31.2. Edge Phenomena 663 §31.3. Simple Computations 671 §31.4. Simplifying the Leray-Serre Spectral Sequence 673 §31.5. Additional Problems and Projects 679
Previous Page Next Page