30 Mar 16:35 2012

## Plug for "Topology and Groupoids"

Ronnie Brown <ronnie.profbrown <at> btinternet.com>

2012-03-30 14:35:09 GMT

2012-03-30 14:35:09 GMT

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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]