2005/01/17 by Wojciech Chachólski, W. Chacholski, W. Pitsch +6
Mathematics · #18G55 (Secondary) #55P60 #55R70 (Primary) 55U35 #Algebraic Topology (math.AT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AT #msc:18G55 #msc:55P60 #msc:55R70 #msc:55U35
paper · pdf · doi:10.48550/arxiv.math/0501250
18 pages
arxiv created 2005/01/17 · openalex publication_date 2005/01/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.