Nonabelian Algebraic Topology

Ronald Brown; Philip J. Higgins; Rafael Sivera

doi:10.4171/083

BooksetmMonograph

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

Buy from €109.00Download PDF

A subscription is required to access this book.

	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 $P$ -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 $ω$ -groupoidsp. 439
	Introduction to Part IIIDownload p. 441
13	The algebra of crossed complexes and cubical $ω$ -groupoidspp. 443–479
14	The cubical homotopy $ω$ -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