Rational homotopy and simply-connected 8-manifolds

Csaba Nagy; Johannes Nordström

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arXiv · 2105.13660

Rational homotopy and simply-connected 8-manifolds

Csaba Nagy·Johannes Nordström

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Abstract

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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Csaba Nagy, Johannes Nordström. 2021-05-28. Rational homotopy and simply-connected 8-manifolds. https://arxiv.org/abs/2105.13660

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