Timeline for Is there a sheaf theoretical characterization of a differentiable manifold?
Current License: CC BY-SA 3.0
9 events
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| Feb 14, 2012 at 14:18 | comment | added | Tom Goodwillie | I actually meant (2) when I said (3). I've edited again to correct that now. | |
| Feb 14, 2012 at 14:17 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| Feb 11, 2012 at 23:47 | comment | added | Daniel Moskovich | This is interesting! What about leaving (3) alone, and trying to replace (2) by a sheaf condition? (these are actually different questions, so I should edit the question to make that clear) | |
| Feb 10, 2012 at 14:35 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| Feb 10, 2012 at 14:26 | comment | added | Georges Elencwajg | Thanks for the clarification in your edit: indeed the structural sheaf has no reason to be acyclic in the holomorphic or algebraic category, and usually isn't (except for Stein or affine manifolds). | |
| Feb 10, 2012 at 14:04 | history | edited | Tom Goodwillie | CC BY-SA 3.0 |
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| Feb 10, 2012 at 11:35 | comment | added | Georges Elencwajg | Dear Tom, I don't understand your sentence "you can't get the paracompactness from properties like acyclicity or flasqueness, because you don't have those properties". Like Daniel, I wonder if you are claiming that acyclicity of the structure sheaf implies or doesn't imply paracompactness. Can you please clarify? | |
| Feb 10, 2012 at 5:23 | comment | added | Daniel Moskovich | So, taking the extreme case, what you're saying is that there exists a Hausdorff topological space $M$ with fine, soft, acyclic sheaf $\mathcal{O}_M$, such that $(M,\mathcal{O}_M)$ is locally isomorphic as a locally ringed space to $(\mathbb{R}^n,\mathcal{O})$, yet $M$ is not paracompact? | |
| Feb 10, 2012 at 5:07 | history | answered | Tom Goodwillie | CC BY-SA 3.0 |