Nonabelian Algebraic Topology
Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids
Ronald Brown
Bangor University, UKPhilip J. Higgins
Durham University, UKRafael Sivera
Universitat de València, Spain
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| FrontmatterDownload pp. i–iv | |
| ContentsDownload pp. v–xi | |
| PrefaceDownload pp. xiii–xv | |
| Prerequisites and reading planDownload pp. xvii–xviii | |
| Historical context diagramDownload pp. xix–xx | |
| IntroductionDownload pp. xxi–xxxv | |
| Part I 1- and 2-dimensional resultsp. 1 | |
| Introduction to Part IDownload pp. 3–4 | |
| 1 | Historypp. 5–30 |
| 2 | Homotopy theory and crossed modulespp. 31–63 |
| 3 | Basic algebra of crossed modulespp. 64–85 |
| 4 | Coproducts of crossed -modulespp. 86–104 |
| 5 | Induced crossed modulespp. 105–141 |
| 6 | Double groupoids and the 2-dimensional Seifert–van Kampen Theorempp. 142–204 |
| Part II Crossed complexesp. 205 | |
| Introduction to Part IIDownload p. 207 | |
| 7 | The basics of crossed complexespp. 209–257 |
| 8 | The Higher Homotopy Seifert–van Kampen Theorem (HHSvKT) and its applicationspp. 258–277 |
| 9 | Tensor products and homotopies of crossed complexespp. 278–323 |
| 10 | Resolutionspp. 324–367 |
| 11 | The cubical classifying space of a crossed complexpp. 368–395 |
| 12 | Nonabelian cohomology: spaces, groupoidspp. 396–437 |
| Part III Cubical -groupoidsp. 439 | |
| Introduction to Part IIIDownload p. 441 | |
| 13 | The algebra of crossed complexes and cubical -groupoidspp. 443–479 |
| 14 | The cubical homotopy -groupoid of a filtered spacepp. 480–512 |
| 15 | Tensor products and homotopiespp. 513–543 |
| 16 | Future directions?pp. 544–551 |
| Appendicesp. 553 | |
| A | A resumé of some category theorypp. 555–576 |
| B | Fibred and cofibred categoriespp. 577–597 |
| C | Closed categoriespp. 598–614 |
| Bibliographypp. 615–642 | |
| Glossary of symbolspp. 643–652 | |
| Indexpp. 653–668 |