Wen Shen

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20242026

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math.AT2026

Loop Space Splittings for Codimensional Sphere Bundles

Wen Shen

In this paper, we establish two loop decomposition theorems for sphere bundles of real vector bundles under appropriate connectivity and characteristic class assumptions. Specifica…

math.AT2026

Loop Space Splittings of Sphere Bundles over Highly Connected Poincaré Complexes

Wen Shen

Let $m > n \geq 2$ , and let $N$ be an $(n - 1)$ -connected $2 n$ -Poincaré complex. In this paper, we establish sufficient conditions under which the loop space of the total space $M$ of…