Author:  Ronald Brown 
 Author's e-mail address: r.brown@bangor.ac.uk
 Author's web page: http://www.bangor.ac.uk/~mas010
 Author's mailing address: 
 Professor Emeritus R. Brown,
 Department of Mathematics,
 University of Wales, Bangor
 Dean St., Bangor, Gwynedd LL57 1UT,
 United Kingdom
 AMS classification number: 18D05,18D15,18G50,55P15,55U40,57M07
 arXive submission number: math.AT/0407275

Abstract: 

We sketch the background to a book with the  title  `Nonabelian
algebraic topology' being written under support of a Leverhulme
Emeritus Fellowship (2002-2004) by the speaker and Rafael Sivera
(Valencia). The aim is to give in one place a full account of 
work  by R. Brown and P.J. Higgins and others since the 1970s 
which defined and applied crossed complexes and cubical higher 
homotopy groupoids to local-to-global problems and homotopy 
classification of maps.  This yields a distinctive account of 
that part of algebraic topology which lies between homology 
theory and homotopy theory, in which the fundamental group and 
its actions plays an essential role, and which allows for 
nonabelian calculations in dimension 2.  This is an extended 
account of a short presentation with this title given at the 
Minneapolis IMA Workshop on `$n$-categories: foundations and 
applications', June 7-18, 2004, organised by John Baez and Peter 
May.