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Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.

8 votes

Two discs with no parallel tangent planes

If I understood your question correctly, I think that the answer is no. In fact, even more is true: if you choose any identification $\varphi \colon \Sigma_1 \to \Sigma_2$ in such a way that the boun …
damiano's user avatar
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19 votes

Compactification of a manifold

A "surface of infinite genus" $S$ is an example of a manifold that is not an open subset of a compact manifold. The reason $S$ cannot be embedded in a compact manifold is straightforward: we can find …
damiano's user avatar
  • 5,137