I would like to know if there are examples of topological manifolds that not admit a smooth atlas, or more generally a differentiable structure of class $C^k$ for $k\geq1$. In the book "Introduction to Manifolds - Loring W. Tu"" the author says that an example of this type is dued to M. Kervaire.
2026-04-12 19:43:21.1776023001
Topological manifold but not "smooth"
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