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arXiv · 2210.17352

Sphere bundles over $4$-manifolds are trivial after looping

Ruizhi Huang
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Abstract

We show that except two special cases, the sphere bundle of a vector bundle over a simply connected $4$-manifold splits after looping. In particular, this implies that though there are infinitely many inequivalent sphere bundles of a given rank over a $4$-manifold, the loop spaces of their total manifolds are all homotopy equivalent.

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Ruizhi Huang. 2022-10-31. Sphere bundles over $4$-manifolds are trivial after looping. https://arxiv.org/abs/2210.17352

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