Homotopy pullback squares up to localization
Abstract
We characterize the class of homotopy pullback squares by means of elementary closure properties. The so called Puppe theorem which identifies the homotopy fiber of certain maps constructed as homotopy colimits is a straightforward consequence. Likewise we characterize the class of squares which are homotopy pullbacks "up to Bousfield localization". This yields a generalization of Puppe's theorem which allows to identify the homotopy type of the localized homotopy fiber. When the localization functor is homological localization this is one of the key ingredients in the group completion theorem.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2005
 DOI:
 10.48550/arXiv.math/0501250
 arXiv:
 arXiv:math/0501250
 Bibcode:
 2005math......1250C
 Keywords:

 Algebraic Topology;
 55P60;
 55R70 (Primary) 55U35;
 18G55 (Secondary)
 EPrint:
 18 pages