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2007 and 2008: 1st volume of a textbook in three Parts, 17 chapters, and 412 pages, available on line

Abstract:

Quote from the Preface of the Book by the Authors:\\ ``Part I includes some of the history of the work on the fundamental group and groupoid, in particular explaining how the van Kampen theorem gives a method of computation of the fundamental group. The remainder of Part I is mainly concerned with the extension of nonabelian work to dimension 2, using the key concept of crossed module-- due to J.H.C. Whitehead in 1946. Part II : Extends the theory of crossed modules to crossed complexes, giving applications which include many basic results in homotopy theory, such as the relative Hurewicz theorem. This Part II is intended as a `handbook' of basic techniques in this border area between homology and homotopy theory. Part III: Introduces the algebraic structure, of a cubical omega-groupoid with connection. The proofs of the results in Part II, and particularly of the van Kampen type theorem, use the concepts of tensor product and homotopy theory of crossed complexes, as well as the concept of a cubical omega-groupoid with connection."

Rights:

Open access: http://www.bangor.ac.uk/~mas010/nonab-t/partI010604.pdf Copyright@ 2004 R. Brown/R. Sivera http://www.bangor.ac.uk/~mas010/nonab-t/partI010604.pdf http://www.bangor.ac.uk/~mas010/nonab-a-t.html http://arxiv.org/PS_cache/math/pdf/0407/0407275v2.pdf http://arxiv.org/abs/math.AT/0407275 http://arxiv.org/PS_cache/math/pdf/0702/0702677v1.pdf

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