Title of Paper: 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

Author(s): Ronald Brown and Philip J. Higgins

AMS Classification numbers: 0F34, 20L13, 20L15, 57S30

Already submitted to the xxx LANL archive, include the id. no.,

 math.AT/0212271

Addresses of Authors:

 Ronald Brown
 Mathematics Division,
 School of Informatics,
 University of Wales, Bangor
 Gwynedd LL57 1UT,  U.K.

 Philip J. Higgins
 Department of Mathematical Sciences,
 Science Laboratories,
 South Rd.,
 Durham, DH1 3LE,  U.K.

Email address of Authors

 r.brown@bangor.ac.uk
 p.j.higgins@durham.ac.uk


Text of Abstract (try for 20 lines or less)

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 (1988
edition). This is a somewhat edited, and in one point (on normal
closures) corrected, version of those sections.

Because of its provenance, this should be read as a graduate text
rather than an article. The Exercises should be regarded as
further propositions for which we leave the proofs to the reader.
It is expected that this material will be part of a new edition of
the book.