Chapter IV. Quadratic modules and homotopy systems of order 4. § 4 Homotopies for quadratic chain maps

Chapters in this book

1. Frontmatter I
2. Chapter I. Homotopy, homology, and Whitehead’s classification of simply connected 4-dimensional CW-complexes 1
3. Chapter II. The CW-tower of categories 32
4. Chapter III. Crossed modules and homotopy systems of order 3 87
5. Chapter IV. Quadratic modules and homotopy systems of order 4. § 1 Quadratic modules 166
6. Chapter IV. Quadratic modules and homotopy systems of order 4. § 2 Free quadratic modules 177
7. Chapter IV. Quadratic modules and homotopy systems of order 4. § 3 Quadratic chain complexes 187
8. Chapter IV. Quadratic modules and homotopy systems of order 4. § 4 Homotopies for quadratic chain maps 191
9. Chapter IV. Quadratic modules and homotopy systems of order 4. § 5 Cofibrations in the category of quadratic chain complexes 205
10. Chapter IV. Quadratic modules and homotopy systems of order 4. § 6 The secondary homotopy addition lemma and a model functor from spaces to quadratic chain complexes 209
11. Chapter IV. Quadratic modules and homotopy systems of order 4. § 7 Homotopy systems of order 4 216
12. Chapter IV. Quadratic modules and homotopy systems of order 4. § 8 The homotopy category of 3-dimensional CW-complexes 220
13. Chapter IV. Quadratic modules and homotopy systems of order 4. § 9 The CW-tower in degree ≤ 4 226
14. Chapter IV. Quadratic modules and homotopy systems of order 4. § 10 The homotopy category of 3-types 229
15. Chapter IV. Quadratic modules and homotopy systems of order 4. § 11 The action of the fundamental group for quadratic chain complexes 230
16. Chapter IV. Quadratic modules and homotopy systems of order 4. § 12 The quadratic chain complex of a product 233
17. Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix A. Some diverse examples and applications of quadratic chain complexes 244
18. Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix B. Quadratic chain complexes and simplicial groups 258
19. Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix C. Reduced and stable quadratic modules 265
20. Chapter IV. Quadratic modules and homotopy systems of order 4. Appendix D. On the homotopy classification of semi free group actions 272
21. Chapter V. Cohomological invariants 279
22. Chapter VI. The cohomology of categories and the calculus of tracks 314
23. Bibliography 369
24. List of Symbols 373
25. Index 377