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

Author(s): Ronald Brown

AMS Classification numbers: 01-01,16E05,18D05,18D35,55P15,55Q05

Already submitted to the xxx LANL archive, include the id. no.,

 math.AT/0212271

Addresses of Authors:

 Ronald Brown
 Mathematics Division,
 School of Informatics,
 University of Wales, Bangor
 Gwynedd LL57 1UT,  U.K.


Email address of Authors

 r.brown@bangor.ac.uk

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.