Nonabelian Algebraic Topology
by: Ronald Brown, Philip J. Higgins, Rafael Sivera
This book aims to present the work on crossed complexes and related higher homotopy groupoids
carried out mainly by the first two authors from 1974 to 2005, resulting in 12 joint papers.
This account also elucidates fully, as did [BH81a], a paragraph near the end of the Introduction
to [Bro67] which referred speculatively to an n-dimensional version of the van Kampen theorem.
The intuition behind that speculation drove the subsequent research, and it was interesting to see
how well it all worked.
The aim became to develop the theories of groupoids and higher groupoids in a similar spirit to
that of combinatorial group theory.
Nonabelian algebraic topology :
homotopy groupoids and filtered spaces
by Ronald Brown, Philip J. Higgins and Rafael Sivera
The papers which give this theory were developed over the period 1971-2001. For a survey of the material to be contained in the book, see the article
`Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems', Proceedings of the Fields Institute Workshop on Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories, September 23-28, Fields Institute Communications 43 (2004) 101-130 (see updated version to appear in Michiel Hazewinkel (ed), Handbook of Algebra vol 6, Elsevier (2008/9)). It will be seen from this article, that the structures which enable the full use of crossed complexes as a tool in algebraic topology are substantial, intricate and interrrelated.
http://ifile.it/1u54sdq/rbrsbookb-e-131008.pdf
