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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 , and let be an -connected -Poincaré complex. In this paper, we establish sufficient conditions under which the loop space of the total space o…
math.AT2025
Manifold structures on highly connected Poincaré complexes
Wen Shen
This paper constructs numerous examples of highly connected Poincaré complexes, each homotopy equivalent to a topological manifold yet not homotopy equivalent to any smooth manifo…