Geodesic
Formality of sphere bundles
Zhou, Jiawei1
1School of Mathematics and Computer Sciences, Nanchang University, Nanchang, China, Beijing Institute of Mathematical Sciences and Applications, Beijing, China
Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2297-2315
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We study the formality of orientable sphere bundles over connected compact manifolds. When the base manifold is formal, we prove that the formality of the bundle is equivalent to the vanishing of the Bianchi–Massey tensor introduced by Crowley and Nordström. As an example, this implies that the unit tangent bundle over a formal manifold can only be formal when the base manifold has vanishing Euler characteristic or a rational cohomology ring generated by one element. When the base manifold is not formal, we give an obstruction to the formality of sphere bundles whose Euler class is reducible.

DOI : 10.2140/agt.2025.25.2297
Keywords: formality, sphere bundle, Bianchi–Massey tensor, obstruction

Zhou, Jiawei  1

1 School of Mathematics and Computer Sciences, Nanchang University, Nanchang, China, Beijing Institute of Mathematical Sciences and Applications, Beijing, China 
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Zhou, Jiawei. Formality of sphere bundles. Algebraic and Geometric Topology, Tome 25 (2025) no. 4, pp. 2297-2315. doi: 10.2140/agt.2025.25.2297

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