Timeline for How to classify the algebras C^∞(M)?
Current License: CC BY-SA 2.5
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| Apr 13, 2010 at 11:32 | comment | added | Martin Brandenburg | the fact that $C^{\infty}$ is full faithful implies that the manifold can be reconstructed from the algebra and every additional structure needed on this algebra can be recovered from the algebra structure. your claim that homeomorphic manifolds yield the same algebra is wrong. $C^{\infty}(M)$ and $C^{\infty}(N)$ are isomorphic as algebras iff $M,N$ are diffeomorphic. | |
| Apr 13, 2010 at 11:03 | history | answered | Miguel | CC BY-SA 2.5 |