Nonabelian algebraic topology

Nonabelian algebraic topology

[Ronnie Brown]

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/ ]

Nonabelian algebraic topology

[Ronnie Brown]

This advertises Part I of a three part book with the above title. We are
putting Part I (with overall TOC) on the web to awake interest and in the
hope of getting comments and suggestions. Details are on

http://www.bangor.ac.uk/~mas010/nonab-a-t.html

Special interest for this list should be the use of higher categorical
structures.


Ronnie Brown and Rafael Sivera Villenueva


 Professor Emeritus R. Brown,
 Department of Mathematics,
 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)

 Centre for the Popularisation of Mathematics:
 http://www.cpm.informatics.bangor.ac.uk/
  (reorganised site with new sculpture animations)