Nonabelian Algebraic Topology

Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids

  • Ronald Brown

    Bangor University, UK
  • Philip J. Higgins

    Durham University, UK
  • Rafael Sivera

    Universitat de València, Spain
Nonabelian Algebraic Topology cover
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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
1Historypp. 5–30
2Homotopy theory and crossed modulespp. 31–63
3Basic algebra of crossed modulespp. 64–85
4Coproducts of crossed PP-modulespp. 86–104
5Induced crossed modulespp. 105–141
6Double groupoids and the 2-dimensional Seifert–van Kampen Theorempp. 142–204
Part II Crossed complexesp. 205
Introduction to Part IIDownload p. 207
7The basics of crossed complexespp. 209–257
8The Higher Homotopy Seifert–van Kampen Theorem (HHSvKT) and its applicationspp. 258–277
9Tensor products and homotopies of crossed complexespp. 278–323
10Resolutionspp. 324–367
11The cubical classifying space of a crossed complexpp. 368–395
12Nonabelian cohomology: spaces, groupoidspp. 396–437
Part III Cubical ω\omega-groupoidsp. 439
Introduction to Part IIIDownload p. 441
13The algebra of crossed complexes and cubical ω\omega-groupoidspp. 443–479
14The cubical homotopy ω\omega-groupoid of a filtered spacepp. 480–512
15Tensor products and homotopiespp. 513–543
16Future directions?pp. 544–551
Appendicesp. 553
AA resumé of some category theorypp. 555–576
BFibred and cofibred categoriespp. 577–597
CClosed categoriespp. 598–614
Bibliographypp. 615–642
Glossary of symbolspp. 643–652
Indexpp. 653–668

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