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arXiv · 2606.03072

Loop Space Splittings for Codimensional Sphere Bundles

Wen Shen
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Abstract

In this paper, we establish two loop decomposition theorems for sphere bundles of real vector bundles under appropriate connectivity and characteristic class assumptions. Specifically, we treat two families of sphere bundles: those arising from rank-$(n-1)$ vector bundles and those from rank-$(n-3)$ vector bundles over closed smooth $n$-manifolds.

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Wen Shen. 2026-06-02. Loop Space Splittings for Codimensional Sphere Bundles. https://arxiv.org/abs/2606.03072

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