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arXiv · 2105.03881

Loop homotopy of $6$-manifolds over $4$-manifolds

Ruizhi Huang
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Abstract

Let $M$ be the $6$-manifold $M$ as the total space of the sphere bundle of a rank $3$ vector bundle over a simply connected closed $4$-manifold. We show that after looping $M$ is homotopy equivalent to a product of loops on spheres in general. This particularly implies the cohomology rigidity property of $M$ after looping. Furthermore, passing to the rational homotopy, we show that such $M$ is Koszul in the sense of Berglund.

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Ruizhi Huang. 2021-05-09. Loop homotopy of $6$-manifolds over $4$-manifolds. https://doi.org/10.2140/agt.2023.23.2369

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