Comments welcome on the following survey: Ronald Brown Crossed complexes and homotopy groupoids as non commutative tools for higher dimensional local-to-global problems Abstract: (This is an extended account of a lecture given at the meeting on `Categorical Structures for Descent and Galois Theory, Hopf Algebras and Semiabelian Categories', Fields Institute, September 23-28, 2002.) 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 non commutative results and compute homotopy types. (27 pages, 81 references) http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/02... http://www.bangor.as.uk/~mas010/fields-art3.pdf -- Professor Emeritus R. Brown, School of Informatics, Mathematics Division, University of Wales, Bangor Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom Tel. direct:+44 1248 382474|office: 382681 fax: +44 1248 361429 World Wide Web: home page: http://www.bangor.ac.uk/~mas010/ (Links to survey articles: Higher dimensional group theory Groupoids and crossed objects in algebraic topology) Raising Public Awareness of Mathematics CDRom Version 1.1 http://www.bangor.ac.uk/~mas010/CDadvert.html Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.informatics.bangor.ac.uk/ 16-Dec-2002 14:20:57 -0400,2371;000000000001-00000000