For Category Bulletin: New Preprint

For Category Bulletin: New Preprint

[categories]

Date: Mon, 8 Sep 1997 16:27:35 +0100 (BST)
From: Ronnie Brown <r.brown@bangor.ac.uk>


Groupoids and Crossed Objects in Algebraic Topology
Ronald Brown

Notes for Lectures at the Summer School on the `Foundations of Algebraic 
Topology', Grenoble, June 14 -July 5, 1997 (71 pages). 
Abstract: 
The notes concentrate on the background, intuition, proof and 
applications of the 2-dimensional Van Kampen Theorem 
(for the fundamental crossed module of a pair), with 
sketches of extensions to higher dimensions.
One of the points stressed is how the extension from 
groups to groupoids leads to an extension from the abelian
homotopy groups to non abelian higher dimensional 
generalisations of the fundamental group, as was sought 
by the topologists of the early part of this century. 
This links with J.H.C. Whitehead's efforts to extend 
combinatorial group theory to higher dimensions 
in terms of combinatorial homotopy theory, and which 
analogously motivated his simple homotopy theory.  

Available from 

http://www.bangor.ac.uk/~mas010/brownpr.html

(gzipped postscript). 

Ronnie Brown

Prof R. Brown, School of Mathematics, 
University of Wales, Bangor      
Dean St., Bangor, Gwynedd LL57 1UT, United Kingdom                               
Tel. direct:+44 1248 382474|office:     382475
fax: +44 1248 383663    
World Wide Web:
home page: http://www.bangor.ac.uk/~mas010/
New article: Higher dimensional group theory


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