preprints: Homotopies and automorphisms...; Local subgroupoids II

preprints: Homotopies and automorphisms...; Local subgroupoids II

[Ronnie Brown]

The following preprints are available on http://arXiv.org

http://arXiv.org/math.CT/0008117
R. Brown, I. Icen
Homotopies and automorphisms of crossed modules of groupoids
ABSTRACT: We give a detailed description of the structure of the actor
2-crossed module related to the automorphisms of a crossed module of
groupoids. This generalises work of Brown and Gilbert for the case of
crossed modules of groups, and part of this is needed for work on
2-dimensional holonomy to be developed elsewhere.
19pp

http://arXiv.org/math.DG/0008165
R. Brown, I. Icen, O.Mucuk
Local subgroupoids II: Examples and properties
ABSTRACT: The notion of local subgroupoid as a generalisation of a local
equivalence relation was defined in a previous paper by the first two
authors. Here we use the notion of star path connectivity for a Lie
groupoid to 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.
These results are required for further applications to holonomy and
monodromy.
18pp
[The first paper is on
http://www.bangor.ac.uk/ma/research/preprints/00/algtop00.html
preprint 00.03, and on math.DG/9808112, and is to appear in Topology and
Appl.]
--
Prof R. Brown,
School of Informatics, Mathematics Division,
University of Wales, Bangor
Dean St., Bangor,
Gwynedd LL57 1UT, United Kingdom
Tel. direct:+44 1248 382474|office:     382475
fax: +44 1248 361429
World Wide Web:
home page: http://www.bangor.ac.uk/~mas010/
(Links to survey articles:
Higher dimensional group theory
Groupoids and crossed objects in algebraic topology)

Symbolic Sculpture and Mathematics:
http://www.bangor.ac.uk/SculMath/
Centre for the Popularisation of Mathematics
http://www.bangor.ac.uk/cpm/