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The research aims to construct examples of highly connected Poincaré complexes that differ from smooth manifolds.

Manifold structures on highly connected Poincaré complexes

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The research aims to construct examples of highly connected Poincaré complexes that differ from smooth manifolds.
Constructed examples of Poincaré complexes
Analyzed their homotopy equivalences
Determined the homotopy type of closed framed manifolds
Identified numerous Poincaré complexes homotopy equivalent to topological manifolds
Proved these complexes are not homotopy equivalent to any smooth manifolds
Characterized closed (4k + 2)-manifolds with Kervaire invariant one for k values 7, 15, and 31

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Demonstrates homotopy equivalences in highly connected Poincaré complexes, suggesting new insights into manifold structures.

Wen Shen (2026) studied this question.

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