Timeline for Isomorphic algebras determine diffeomorphic manifolds
Current License: CC BY-SA 3.0
5 events
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| Feb 10, 2017 at 20:54 | comment | added | Eugene Lerman | I don't know a direct proof. My answer slyly suggested that looking at the algebra of functions on a smooth manifold as an algebra is a bit silly and that $C^\infty$ rings provide a better framework. But since I cheated, here is an answer to the question you asked: Theorem 2.3 on p. 34 of $C^\infty$-Differentiable Spaces by Juan A. Navarro Gonzalez and Juan B. Sancho de Salas (Springer LNM 1824). | |
| Feb 10, 2017 at 17:30 | comment | added | Totentanz | I have already accepted your answer, however I realized that there is one subtle thing. As you mentioned the notion of $C^{\infty}$ ring is more general than just smooth functions on manifold however the notion of morphism in this category appears to be more restrictive. So how one can prove that any homomorphism of algebras is automatically a $C^{\infty}$ morphism (as defined in Moerdijk's book)? | |
| Feb 4, 2017 at 1:13 | history | edited | José Figueroa-O'Farrill | CC BY-SA 3.0 |
changed 8.2 to 2.8
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| Feb 3, 2017 at 21:58 | vote | accept | Totentanz | ||
| Feb 3, 2017 at 21:27 | history | answered | Eugene Lerman | CC BY-SA 3.0 |