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... 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 20-Dec-2002 14:53:27 -0400,1780;000000000001-00000000