U.W. Bangor - School of Informatics - Mathematics Preprints 2000
00.03 : BROWN, R. & ICEN, I.
Lie local subgroupoids and their monodromy
The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendability of local Lie morphisms.
Published in:Topology and its Applications (to appear)
ftp access: gzipped postscript - sub00.ps.gz
00.04 : PORTER, T.
Atlases of groupoids and global actions
00.06 : BROWN, R. & ICEN, I.
Examples and coherence properties of local subgroupoids
Abstract:The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the authors. Here we give an important new class of examples, generalising the local equivalence relation of a foliation, and develop in this new context basic properties of coherence, due earlier to Rosenthal in the special case.
ftp access: gzipped postscript - coh-l-g2.ps.gz
00.17 : BROWN, R., BULLEJOS, M. & PORTER, T.
Crossed complexes, free crossed resolutions and graph products of groups
Abstract:The category of crossed complexes gives an algebraic model of the category of CW-complexes and cellular maps. We explain basic results on crossed complexes which allow the computation of free crossed resolutions of graph products of groups, and of free products with amalgamation, given free crossed resolutions of the individual groups.
ftp access:xxx-archive : http://uk.arXiv.org/abs/math.AT/0101220
Published in:Recent advances in group theory and low-dimensional topology, Proc. German-Korean workshop at Pusan, August 2000,
Research and Exposition in Mathematics, Vol.27, J Mennicke & Moo Ha Woo (eds.) (2003) 11-26,
Heldermann Verlag, ISBN 388538227X .
00.25 : INASSARIDZE, N. & PORTER, T.
Abelianization of crossed n-cubes and generalised Hopf formula
00.29 : FORRESTER-BARKER, M.
Group objects and internal categories
Abstract:Algebraic structures such as monoids, groups and even categories can be formulated within a category using commutative diagrams.
In many common categories these reduce to familiar cases.
In particular, group objects in Grp are abelian groups, while internal categories in Grp are equivalent both to group objects in Cat and to crossed modules of groups. In this exposition we give an elementary introduction to some of the key concepts in this area.