Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems

Details Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems

2002-12-19

arxiv.org/abs/math/0212274v7

Fields Institute Communications 43 (2004) 101-130

Mathematics

Algebraic Topology

30 pages, Latex2e, xypic v2. Replacement 14/07/07 More references. v3 Detailed changes 22/01/08 Change in Main Diagram. More r

Scientific paper

We outline the main features of the definitions and applications of crossed
complexes and cubical $\omega$-groupoids with connections. These give forms of
higher homotopy groupoids, and new views of basic algebraic topology and the
cohomology of groups, with the ability to obtain some non commutative results
and compute some homotopy types.

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