Timeline for Riemannian manifolds etc. as locally ringed spaces?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2019 at 20:17 | history | edited | Qfwfq | CC BY-SA 4.0 |
deleted 8 characters in body; edited title
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| Aug 3, 2019 at 19:18 | comment | added | Mishkaat | From scheme theoretic perspective, how do wish to 'deal' with additional structures like metrics, symplectic forms, hermitian or kahler structures? | |
| Nov 11, 2011 at 1:17 | comment | added | David Carchedi | I'm quite interested in this question. Made any progress since Feb? | |
| Feb 27, 2011 at 18:29 | comment | added | Qfwfq | @JohanesEbert: recovering $g$ up to conformal equivalence would already be nice. And what about LRS morphisms: would they correspond to conformal mappings? | |
| Feb 27, 2011 at 18:26 | comment | added | Qfwfq | @Zack: ya.. it looks like so. Perhaps my definition is just useless. But I don't know how morphisms of symplectic/Riemannian manifolds induce homomorphisms on that sheaves. | |
| Feb 27, 2011 at 18:18 | comment | added | Zack | Isn't $\mathcal{O}[\omega]$ just $\mathcal{O}[x]/x^{n+1}$? | |
| Feb 27, 2011 at 17:40 | comment | added | Johannes Ebert | You cannot recover $g$ from $\mathcal{O}[g]$, only up to conformal equivalence. | |
| Feb 27, 2011 at 16:31 | comment | added | Qfwfq | @André: In the theory of "supermanifolds" people already use sheaves of $\mathbb{Z}/2\mathbb{Z}$-graded rings. And there are some recent theories of "derived manifolds" (of which I don't know anything). But my question was perhaps more down to earth. Anyway, why do you suggets using differential graded rings? Is it to keep track that the "generator" $g$ in $\mathcal{O}_X[g]$ is placed in (tensor) degree 2? | |
| Feb 27, 2011 at 16:24 | comment | added | André Henriques | Maybe it could be useful to generalize the notion of locally ringed space, and allow "structure sheaves" with values in categories other than rings (e.g. differential graded rings). | |
| Feb 27, 2011 at 16:08 | history | asked | Qfwfq | CC BY-SA 2.5 |