Presentation of homotopy types under a space

2010/05/26 by Hans-Joachim Baues, Baues, Hans-Joachim, Beatrice Bleile +1
Mathematics · #18B40 #55-02 #55P05 #55P15 #55Q15 #55Q35 #55U35 #Algebraic Topology (math.AT) #FOS: Mathematics #math.AT #msc:18B40 #msc:55-02 #msc:55P05 #msc:55P15 #msc:55Q15 #msc:55Q35 #msc:55U35

paper · pdf · doi:10.48550/arxiv.1005.4810

21 pages

arxiv created 2010/05/26 · arxiv updated 2010/05/27

Abstract

We compare the structure of a mapping cone in the category Top^D of spaces under a space D with differentials in algebraic models like crossed complexes and quadratic complexes. Several subcategories of Top^D are identified with algebraic categories. As an application we show that there are exactly 16 essential self--maps of S² x S² fixing the diagonal.

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• Modelling and Computing Homotopy Types: I