Homotopy pull-back squares up to localization

Details Homotopy pull-back squares up to localization Homotopy pull-back squares up to localization

2005-01-17

arxiv.org/abs/math/0501250v1

Mathematics

Algebraic Topology

18 pages

Scientific paper

We characterize the class of homotopy pull-back 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 pull-backs "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.

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