Sullivan minimal models of classifying spaces for non-formal spaces of small rank

2015/04/27 by Hirokazu Nishinobu, Nishinobu, Hirokazu, Toshihiro Yamaguchi +1
Mathematics · #55P62 #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Cohomology #Combinatorics #Computer science #Discrete mathematics #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Integer (computer science) #Mathematics #Programming language #Pure mathematics #Rank (graph theory) #Rational number #Space (punctuation) #math.AT #msc:55P62

paper · pdf · doi:10.48550/arxiv.1504.07002

15 pages

arxiv created 2015/04/27 · openalex publication_date 2015/04/27 · arxiv updated 2015/04/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We consider certain rational homotopical conditions of simly connected CW complex X such that the rational cohomology of the classifying space Baut₁X for fibrations with two-stage fibre X is (not) free. First, we consider when is Baut₁X a rational factor of Baut₁(X× Sⁿ) for an odd-integer n and observe for a non-formal elliptic space X of rank 3. Second, we compute the Sullivan minimal models of Baut₁X when X are certain non-formal pure spaces of rank 5.

Citations

• Deformation theory and rational homotopy type
• Infinitesimal computations in topology

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