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Manifold structures on highly connected Poincaré complexes

Published 31 Jul 2025 in math.AT and math.GT | (2507.23228v1)

Abstract: This paper constructs numerous examples of highly connected Poincar\'{e} complexes, each homotopy equivalent to a topological manifold yet not homotopy equivalent to any smooth manifold. Furthermore, we determine the homotopy type of any closed $2k$-connected framed $(4k+2)$-manifold with Kervaire invariant one for $k=7,15,31$.

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Authors (1)

  1. Wen Shen 

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