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Rational homotopy and simply-connected 8-manifolds
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Rational homotopy and simply-connected 8-manifolds
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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 S^2 x S^6 are determined up to torsion by the value of P.
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Cited by 1 Pith paper
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Minimal Unital Cyclic $C_\infty$-Algebras and the Real and Rational Homotopy Type of Closed Manifolds
For (r−1)-connected closed manifolds of dimension n ≤ l(r−1)+2, rational homotopy type is determined by the cohomology ring and the minimal cyclic C∞-algebra enhancement up to isotopy modulo l−2.
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