Ronnie Brown | 30 Mar 16:35 2012

Plug for "Topology and Groupoids"

I hope it is OK to the list to make another plug for my book
   "Topology and Groupoids" ISBN: 1-4196-2722-8
available from amazon.com at $31.99 new.  Not having the usual services
of a publisher, I have to do the publicity myself, and I notice some
university  libraries do not have a copy. .

There is a review for the Mathematical Association of America at
http://mathdl.maa.org/mathDL/19/?pa=reviews&sa=viewBook&bookId=69421
which ends:

" /Topology and Groupoids/ is an impressive work which should be given a
wide circulation. "

If it is not in your library, please recommend it!  It is being used as
a course text in several places (Harvard, Zululand, ...).

The first part of the book is a geometric approach to general topology,
with an emphasis on motivation for definitions and theorems and  on
topologies defined so as to be able to construct continuous functions,
i.e. a categorical approach.

The second part of the book shows that much of 1-dimensional homotopy is
well expressed using the language of groupoids, for example:

the van Kampen theorem for the non-connected case, e.g. the circle,
leading to a proof of the Jordan Curve Theorem;

basics of combinatorial groupoid theory;

operations of the fundamental groupoid on sets of homotopy classes,
leading to a gluing theorem for homotopy equivalences;

covering spaces, related to covering morphisms of groupoids;

orbit spaces, related to orbit groupoids (for a discontinuous action on
a Hausdorff which is nice locally, the fundamental groupoid of the orbit
space is the orbit groupoid of the fundamental groupoid);

There are over 500 exercises, 114 figures, numerous diagrams.

Many other features of the book are  not available in other texts, for
example fibrations of groupoids, and the associated exact sequences; a
convenient category of spaces in the non-Hausdorff case. For more
details, see
www.bangor.ac.uk/r.brown/topgpds.html

Ronnie Brown

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Gmane