2021/05/28 by Csaba L. Nagy, Csaba Nagy, Nagy, Csaba +2
Mathematics · Physics and Astronomy · #55P62 #57N65 #57R19 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GT #msc:55P62 #msc:57N65 #msc:57R19
paper · pdf · doi:10.48550/arxiv.2105.13660
17 pages. v2: minor corrections
openalex publication_date 2021/05/28 · arxiv created 2021/07/02 · arxiv updated 2021/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce a rational homotopy invariant P of a topological space, which is a quintic tensor on the cohomology. For n > 1, formality of a closed (n-1)-connected manifold of dimension up to 5n-2 is equivalent to vanishing of P and the Bianchi-Massey tensor introduced by Crowley and the second author arXiv:1505.04184. We show also that elements of the group of closed simply-connected spin 8-manifolds with the cohomology of an r-fold connected sum of S2 x S6 are determined up to torsion by the value of P.