Subject: Re: book suggestions: beginning algebraic topology Date: Thu, 05 Sep 2002 16:48:56 +0100 From: Ronnie Brown > Shameless self-promotions are also welcome! Noting this, I should advertise my book Topology: a geometric account of general topology, homotopy types, and the fundamental groupoid, Ellis Horwood, Chichester (1988) 460 pp. unfortunately out of print but if there were lots of buyers I could consider printing versions while I get on sometime with completing a new latex edition (a lot done). This book consistently exploits the fundamental groupoid, and presents the (heretical?) view that all of 1-dimensional homotopy theory is better presented in terms of groupoids rather than groups (e.g. more powerful theorems with simpler proofs). This is still the only source, for example, for the theorem of Brown and Higgins on the fundamental groupoid of an orbit space by a discontinuous action of a discrete group, with which you can really calculate. I refer to Math Reviews for a review (90k:54001). Ronnie Brown Don Davis wrote: > > Subject: beginning algebraic topology > Date: Fri, 30 Aug 2002 01:51:10 +0000 > From: "Kostas. - - -" > > I brought to bear in mind the following, concerning algebraic topology > at > the beginning graduate level; and hoping that forum could dwell on for > a > few seconds and write a blurb or two in response (which, by the way, > would > be greatly appreciated): with so many existing texts on the market (old > and > new, constituting some reprinted classics, and others harder to find), > which would you recommend as required reading (say, for a first course, > assuming a modest background in algebra [if not, then I'm sure Massey > would > do]). I tend to favour the homotopical approach taken by authors, > which > gives an added impetus to a first exposition, as far as I'm concerned. > > Shameless self-promotions are also welcome! > > Again, thanks, > A. Markos > McGill U. -- 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 http://www.bangor.ac.uk/~mas010/CDadvert.html Symbolic Sculpture and Mathematics: http://www.cpm.informatics.bangor.ac.uk/sculmath/ Centre for the Popularisation of Mathematics http://www.cpm.informatics.bangor.ac.uk/