Subject: Bangor WWW Pages

From: categories <[email-masked]>
Date: Wed, 24 Jan 1996 20:25:10 -0400 (AST)

Date: Wed, 24 Jan 1996 16:36:43 +0000
From: "Prof R. Brown" <[email-masked]>

We now have some material available on the world wide web for downloading
as postscript files. The School of Mathematics, University of Wales, Bangor
may be accessed at http://www.bangor.ac.uk/ma/

The following papers  are available as postcript files 
via R. Brown's home page
http://www.bangor.ac.uk/~mas010/home.html

R. Brown and W. Dreckmann,  
``Domains of data and domains of terms in AXIOM''. 
Abstract: This gives a general account and the source Axiom 2.0 code for 
directed graphs, free categories, free groupoids, which will give
an impression of coding in Axiom. 

R. Brown and O. Mucuk, 
``The monodromy groupoid of a Lie groupoid'',  
{\em Cah. Top. G\'eom. Diff. Cat}, 36 (1995) 345-369. 
Abstract:  We show that under general
circumstances, the disjoint union of the universal covers of the
stars of a Lie groupoid admits the structure of a Lie groupoid,
such that the projection has a monodromy property on the
extension of local smooth morphisms. This completes a detailed
account of results announced by J Pradines. 

R. Brown and O. Mucuk, 
``Foliations, locally Lie groupoids, and holonomy'',  
{\em Cah. Top. G\'eom. Diff. Cat}, (1996) (to appear).  
Abstract:  We show that a paracompact foliated manifold 
determines a locally Lie groupoid (or piece of a differentiable 
groupoid, in the sense of Pradines). This allows for the construction 
of holonomy and monodromy groupoids of a foliation to be seen as 
particular cases of constructions for locally Lie groupoids.

R. Brown, 
``Representation and computation for crossed modules'', 
Proceedings {\em Cat\'egories, Algebres, Esquisses, Neo-esquisses}, Caen, 
1994, 6pp.
Abstract: We argue for the need to develop `structural computation', to
handle the translation of algebraic structures between equivalent
categories. This is illustrated with the problem of the tensor product in
the equivalent categories of crossed modules over groupoids, double
groupoids with connection, 2-groupoids. 

R. Brown, M. Golasinski, T.Porter, and A.P.Tonks, 
``On function spaces of equivariant maps and the equivariant 
homotopy theory of crossed complexes.'' 18pp  

Abstract: This paper gives an equivariant version of the homotopy
theory of crossed complexes for the case of a discrete group action.  The
applications generalise work on equivariant Ellenberg-MacLane spaces,
including the non-abelian case of dimension 1, and on local systems.  It
also generalises the theory of equivariant 2-types, due to Moerdijk and
Svensson.  Further we give results not just on the homotopy classification
of maps, but also on the homotopy types of certain equivariant function
spaces. (Indag. Math. (to appear))

R. Brown and T. Porter, 
``On the Schreier theory of non-abelian extensions: generalisations 
and computations'', 21pp 
Abstract: Classically, a Schreier 2-cocycle for a group G involves
functions on the 3-fold and 2-fold products of G with itself. 
We show how a crossed resolution may be used to give smaller and
more computable presentations of such cocycles, which are determined by 
a presentation of G and identities among relations. This is a
modern expression of ideas of Turing, 1938. 

R. Brown and C.D.Wensley, 
``Computing crossed modules induced by an inclusion of a 
normal subgroup, with applications to homotopy 2-types'', 9pp 
Abstract: We suppose M, P are normal subgroups of a group Q and prove 
directly a value for the crossed Q-module induced from the 
crossed P-module M by the inclusion of P in Q. Using methods of free 
crossed resolutions, we calculate explicitly the k-invariant of 
this induced crossed module, in the case when Q/P is finite cyclic. 
We also use coproducts of crossed P-modules to obtain some general
results on induced crossed modules, again when P is normal in Q. 
These results are applied to the 2-type of  homotopy pushouts 
of certain maps of classifying spaces of discrete groups. 
This continues work of a previous paper, published in TAC, 1995, no.3. 

R. Brown and G. Janelidze, 
``Van Kampen theorems  for categories of covering morphisms in lextensive 
categories'', 9pp, (J. Pure Applied Algebra, to appear). 
Abstract: 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. 

R. Brown and G. Janelidze, 
``Galois theory of second order covering maps of simplicial sets'', 10pp, 
submitted, 1995. 
Abstract: 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. 

The following papers  are available as postcript files 
via T. Porter's home page
http://www.bangor.ac.uk/~mas013/home.html

Bangor Maths Preprint No. 95.08
Spaces of maps into classifying spaces for equivariant
crossed complexes.
Authors: R. Brown, M. Golasinski, T. Porter, and A. Tonks
September 13, 1995 (see above) 
Keywords: Equivariant homotopy, crossed complexes
AMS Subject Classification:  55P91, 55U10, 55U35

Bangor Maths Preprint No.95.09
Title: Categorical Aspects of Equivariant Homotopy
Authors:.-M. Cordier and T. Porter
Date: September 13, 1995
Abstract:  Using the theory of homotopy coherent Kan extensions,
results of Elmendorf and Dwyer and Kan are generalised.  This
produces simplicially enriched equivariant versions of the
singular complex / geometric realisation adjunction of the non-
equivariant theory.
Keywords: Homotopy coherent Kan extension, simplicially enriched
categories, G-equivariant homotopy
AMS Subject Classification: 55P91, 18G55, 18D20, 18G30
Type of file:  LATEX or dvi
No. of pages:  18

Bangor Maths Preprint No. 95.10
Title:  Homotopy coherent category theory
Authors:  J.-M. Cordier and T Porter
Abstract: This article is an introduction to the categorical theory
of homotopy coherence.  It is based on the construction of the
homotopy coherent analogues of end and coend, extending ideas of
Meyer and others.  The paper aims to develop homotopy coherent
analogues of many of the results of elementary category theory, in
particular it handles a homotopy coherent form of the Yoneda lemma
and of Kan extensions.  This latter area is linked with the theory
of generalised derived functors.
Keywords: Simplicially enriched categories, Homotopy coherent ends
and coends, Yoneda lemma 
AMS Subject Classification:  18D20, 18D05, 18G30, 18A99
Type of file: dvi, or Postscript
No. of pages:  54

Bangor Maths Preprint No. 95.11
Title:    Interpretations of Yetter's notion of G-coloring: 
          simplicial fibre bundles and non-abelian cohomology
Authors:  T Porter
Date:  October 11, 1995
Abstract: This paper notes and explores the connection between
Yetter's notion of G-coloring where G is either a finite group or
a finite `Categorical group' and the theory of simplicial fibre
bundles.  This allows an interpretation of Yetter's topological
quantum field theory in terms of equivalence classes of simplicial
fibre bundles.  If G is a finite categorical group, these fibre
bundles have interesting lifting properties and their fibres are
groupoids.  Using recent results and descriptions of non-abelian
cohomology due to Breen and Duskin, these fibre bundles are linked
with non-abelian cocycles with coefficients in G.
Keywords:  Topological Quantum Field Theory, fibre bundle, non-
abelian cohomology
AMS Subject Classification:  81T99, 57N70, 55R99
Type of file: Postscript  or dvi.
No. of pages:  30

Prof R. Brown                                   
School of Mathematics                            
Dean St                                           
University of Wales                          
Bangor                                             
Gwynedd LL57 1UT                             
UK
Tel: (direct)  +44 1248 382474  
  (office) +44 1248 382475
  Fax: +44 1248 355881
  email: [email-masked]
wwweb: http://www.bangor.ac.uk/~mas010/home.html
wwweb for maths: http: //www.bangor.ac.uk/ma