On manifolds homeomorphic to spheres

Somnath Basu; Sachchidanand Prasad

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arXiv · 2509.13008

On manifolds homeomorphic to spheres

Somnath Basu·Sachchidanand Prasad

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Abstract

We prove a result analogous to Reeb's theorem in the context of Morse-Bott functions: if a closed, smooth manifold $M$ admits a Morse-Bott function having two critical submanifolds $S^k$ and $S^l$ ($k \neq l$), then $M$ has dimension $k+l+1$ and is homeomorphic to the standard sphere $S^{k+l+1}$ but not necessarily diffeomorphic to it. We also prove similar results for projective spaces over the real numbers, complex numbers and quaternions.

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BibTeX RIS

Somnath Basu, Sachchidanand Prasad. 2025-09-16. On manifolds homeomorphic to spheres. https://arxiv.org/abs/2509.13008

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