New answers tagged smooth-manifolds
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Compactification of a product of manifolds
There is a "smoothing corners" or "rounding corners" technique introduced by John Milnor. See Differentiable structures, Mimeographed Notes, Princeton University, Princeton, N. J., ...
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Compactification of a product of manifolds
Yes, the quotient $C_M = \overline{M} \times \overline{\mathbb{R}} / \left\{\{x\} \times \overline{\mathbb{R}} : x \in \partial\overline{M}\right\}$ seems to do the job, where I mean that the points ...
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A sufficient condition for a collection of open sets of a manifold to contain all open sets
Yes, it is true that $\mathcal{U}$ contains all open sets of $M$. The proof is a minor modification of Weiss's argument, and proceeds in several steps.
Step1
We show that every open set of $M$ ...
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Detecting a "bad map" in Fintushel-Stern knot surgery
There is nothing inherently "bad" with other choices. My guess is that Fintushel and Stern chose this identification for three reasons: first, they can give a nice formula for how the ...
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