Timeline for What properties should $C(M,\mathbb{R})$ have when $M$ is a $n$-dimensional manifold?
Current License: CC BY-SA 4.0
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| Jul 1, 2021 at 23:07 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Jul 1, 2021 at 23:06 | comment | added | Dmitri Pavlov | @PedroLauridsenRibeiro: Yes, this was already discussed in this answer: mathoverflow.net/questions/14877/… | |
| Jul 1, 2021 at 16:46 | comment | added | Pedro Lauridsen Ribeiro | Regarding Milnor's exercise, it leaves open the question of how to characterize the algebra of smooth real-valued functions on a second countable Hausdorff (paracompact) smooth manifold among all commutative $\mathbb{R}$-algebras. In other words, how to intrinsically characterize the image of this (full faithful) contravariant functor from this category of manifolds to the category of commutative $\mathbb{R}$-algebras, apart from the tautological characterization as being the image of such a functor? | |
| Jul 1, 2021 at 15:07 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Jul 1, 2021 at 14:34 | comment | added | Dmitri Pavlov | @BranimirĆaćić: Of course! I added a link to your answer to my question about this. | |
| Jul 1, 2021 at 14:33 | history | edited | Dmitri Pavlov | CC BY-SA 4.0 |
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| Jun 30, 2021 at 23:41 | comment | added | Branimir Ćaćić | One small correction: it’s for compact orientable manifolds. It remains an open fundamental question in noncommutative geometry à la Connes as to how to accommodate nonorientable noncommutative manifolds. | |
| Jun 30, 2021 at 20:47 | history | answered | Dmitri Pavlov | CC BY-SA 4.0 |