Subject: topology discussion list
Date: Thu, 19 Dec 2002 17:04:05 +0000
From: Ronnie Brown
New preprint:
R. Brown and P.J. Higgins
TITLE: The fundamental groupoid of the quotient of a Hausdorff space by a
discontinuous action of a discrete group is the orbit groupoid of the
induced action
ABSTRACT: The main result is that the fundamental groupoid of the orbit
space of a discontinuous action of a discrete group on a
Hausdorff space which admits a universal cover is the orbit
groupoid of the fundamental groupoid of the space. We also
describe work of Higgins and of Taylor which makes this result
usable for calculations. As an example, we compute the fundamental
group of the symmetric square of a space.
The main result, which is related to work of Armstrong, is due to
Brown and Higgins in 1985 and was published in sections 9 and 10
of Chapter 9 of the first author's book on Topology
(Ellis Horwood, 1988). This is a somewhat edited, and in one point (on
normal closures) corrected, version of those sections. Since the
book is out of print, and the result seems not well known, we now
advertise it here.
It is hoped that this account will also allow wider views of
these results, for example in topos theory and descent theory.
math.AT/0212271
http://www.informatics.bangor.ac.uk/public/mathematics/research/preprints/02/algtop02.html#02.25
http://www.bangor.ac.uk/~mas010/orbitgpdxx.pdf
Other Information: 1) A previous announcement of fields-art3.pdf had a url
of bangor.as.uk/~mas010/fields-art3.pdf instead of bangor.ac.uk
2. Our web sites on sculpture and knots have just been reorganised and
given a new look by Mike Yates under an EPSRC grant. There are new
animations, and navigation is much easier. Have a look! (see below)
--
Professor Emeritus 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: 382681
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)
Raising Public Awareness of Mathematics CDRom Version 1.1
Symbolic Sculpture and Mathematics:
Centre for the Popularisation of Mathematics
http://www.cpm.informatics.bangor.ac.uk/centre/index.html