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U.W. Bangor - School of Informatics - Mathematics Preprints 1997

Algebraic topology

97.01 : BROWN, R.

Higher-dimensional group theory

An on-line web document

97.07 : BROWN, R. and WENSLEY, C.D.,

On the computation of induced crossed modules


We give the reasons for embarking on the computation of crossed modules as given in a recent GAP package XMOD. We describe some of the facilities in this package and discuss some of the computational issues involved in computing crossed modules induced over subgroup inclusions.

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ftp access:

97.11 : MUTLU, A.

Peiffer pairings in the Moore complex of a simplicial group

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U W Bangor PhD thesis (June 1997)


gzipped postscript of the thesis:

97.15 : BROWN, R. and JANELIDZE, G.

Van Kampen theorems for categories of covering morphisms in lextensive categories


We show that lextensive categories are a natural setting for statements and proofs of the ``tautologous'' Van Kampen theorem, in terms of coverings of a space.

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J. Pure Applied Algebra, 119 (1997) 255-263

gzipped Postscript file:

97.16 : BROWN, R. and JANELIDZE, G.

Galois theory of second order covering maps of simplicial sets


We give a version for simplicial sets of a second order notion of covering map, which bears the same relation to the usual coverings as do groupoids to sets. The Generalised Galois theory of the second author yields a classification of such coverings by the action of a certain kind of double groupoid.

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J Pure and Applied Alg 135 (1999) 23-31.

gzipped Postscript file:

97.20 : BROWN, R.

Groupoids and crossed objects in algebraic topology

Notes for lectures at the Summer School in Algebraic Topology, Grenoble, June 15 - July 5, 1997. (66 pages).


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.

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Homology, homotopy and applications 1 (1999) 1-78.

gzipped Postscript file

97.30 : LAMBE, L.A.

An algorithm for calculating cocycles


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