On spherical fibrations and Poincare complexes

Wen Shen

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arXiv · 2406.16019

On spherical fibrations and Poincare complexes

Wen Shen

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Abstract

In this paper, we prove that certain spherical fibrations over certain CW-complexes are stably fibre homotopy equivalent to $\mm{TOP}$-spherical fibrations (see Definition 1,1). Applying this result, we get a sufficient condition for whether a Poincar$\mm{\acute{e}}$ complex is of the homotopy type of a topological manifold. Moreover, we present the classification for some highly connected manifolds by the homotopy types of highly connected Poincar$\mm{\acute{e}}$ complexes.

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Wen Shen. 2024-06-23. On spherical fibrations and Poincare complexes. https://arxiv.org/abs/2406.16019

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