Author: Ronald Brown

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

Abstract: 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 in non simply connected situations.

Author's address: School of Computer Science, Bangor University, Dean St., Bangor
Gwynedd Ll57 1UT, UK

Web page: www.bangor.ac.uk/r.brown

Futher information: This is a revised version (2008) of  a paper
published in  Fields Institute Communications 43 (2004) 101-130,
which was an extended account of a lecture given at the meeting on
`Categorical Structures for Descent, Galois Theory, Hopf algebras
and semiabelian categories', Fields Institute, September 23-28,
2002. The author is grateful for support from the Fields Institute
and a Leverhulme Emeritus Research Fellowship, 2002-2004, and to M.
Hazewinkel for helpful comments on a draft. This paper is to appear
in Michiel Hazewinkel (ed.), Handbook of Algebra, volume 6,
Elsevier, 2008/2009.

MATHEMATICS SUBJECT CLASSIFICATION: 01-01,16E05,18D05,18D35,55P15,55Q05

arXiv: math/0212274