Nonabelian algebraic topology
The following is now on the EMS web site: http://www.ems-ph.org/books/book.php?proj_nr=3D130 EMS Tracts in Mathematics Vol. 15 /Ronald Brown (Bangor University, UK) Philip J. Higgins (Durham University, UK) Rafael Sivera (Universitat de Val=E8ncia, Spain)/ Nonabelian Algebraic Topology Filtered Spaces, Crossed Complexes, Cubical Homotopy Groupoids ISBN 978-3-03719-083-8 DOI 10.4171/083 August 2011, 703 pages, hardcover, 17 x 24 cm. 98.00 Euro (distribution via the AMS in October, 2011) The EMS allows a full pdf (with hyperref) on my web page. This proposed new foundation for algebraic topology gives new results,=20 including nonabelian calculations of homotopy 2-types (as crossed=20 modules), on the border between homology and homotopy. As one=20 indication of this, the Relative Hurewicz Theorem is seen as a Corollary=20 of a general Seifert-van Kampen Theorem, whose proof via a cubical=20 homotopy groupoid of a filtered space is at the centre of this approach. One aim is a framework for specific calculations, e.g. of homotopy=20 classes of maps, involving the action of the fundamental group. Ronnie Brown www.bangor.ac.uk/r.brown [For admin and other information see: http://www.mta.ca/~cat-dist/ ]
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Ronnie Brown