Timeline for Computing $H^*(BDiff(W_{\infty},D^{\infty});\mathbb{Q})$ via Mumford-Morita-Miller classes
Current License: CC BY-SA 4.0
20 events
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| Oct 1, 2018 at 15:00 | review | Close votes | |||
| Oct 6, 2018 at 3:05 | |||||
| Sep 25, 2018 at 2:57 | history | edited | Sergio Charles | CC BY-SA 4.0 |
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| Aug 15, 2018 at 3:33 | history | edited | Sergio Charles | CC BY-SA 4.0 |
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| Aug 9, 2018 at 0:42 | vote | accept | Sergio Charles | ||
| Aug 6, 2018 at 3:26 | history | edited | Sergio Charles | CC BY-SA 4.0 |
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| Aug 6, 2018 at 3:23 | comment | added | user80296 | I don't understand what you mean by "compute the MMM classes". The definition of $\kappa_c$ is given on page 2 of the paper you link to, and the statement of the theorem is that those classes generate and are algebraically independent, as $c$ ranges over the set $\mathcal{B}$. I don't think there's more to say. | |
| Aug 5, 2018 at 23:27 | history | edited | Sergio Charles | CC BY-SA 4.0 |
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| Aug 5, 2018 at 16:16 | answer | added | Sergio Charles | timeline score: 0 | |
| Aug 5, 2018 at 2:05 | comment | added | Sergio Charles | I see, thanks so much for your help! @AllenHatcher | |
| Aug 5, 2018 at 1:50 | comment | added | Allen Hatcher | In Definition 1.1 of that paper the dimension of the manifold $W_g$ (which is $2n$, not $n$ as I mistakenly said in my previous comment) is fixed and one is considering embedded submanifolds of ${\mathbb R}^N$ diffeomorphic to $W_g$. Then one lets $N$ go to infinity via the natural inclusion of ${\mathbb R}^N$ in ${\mathbb R}^{N+1}$, so submanifolds of ${\mathbb R}^N$ are regarded as submanifolds of ${\mathbb R}^{N+1}$. However the dimension $2n$ of the submanifolds is not changing. There is no natural way to let $n$ go to infinity in this construction. | |
| Aug 5, 2018 at 0:53 | comment | added | Sergio Charles | Hello Dr. Hatcher! I believe such a map is described in Definition 1.1 of this paper. It uses a slightly different notation; however, I think the maps are equivalent (I am probably wrong, however). @AllenHatcher | |
| Aug 5, 2018 at 0:32 | comment | added | Allen Hatcher | If you mean to take the limit as $n$ goes to $\infty$ you need a way to map diffeomorphisms of the $n$-dimensional manifolds $W^n_g$ to diffeomorphisms of the $(n+1)$-dimensional manifolds $W_g^{n+1}$. It seems unlikely that any interesting map like this could exist. What map do you have in mind? | |
| Aug 4, 2018 at 22:26 | history | edited | Sergio Charles | CC BY-SA 4.0 |
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| Aug 4, 2018 at 22:25 | comment | added | Sergio Charles | Oh, I see. Sorry, that is my mistake; I meant the former with $n=\infty$. @ArunDebray | |
| Aug 4, 2018 at 22:10 | comment | added | Arun Debray | Right, but $g$ doesn't appear in its expression. Did you mean $\varprojlim_g H^*(\mathit{BDiff}(W_g, D^{2n}); \mathbb Q)$ or $\varprojlim_g H^*(\mathit{BDiff}(W_\infty, D^\infty); \mathbb Q)$? | |
| Aug 4, 2018 at 21:30 | comment | added | Sergio Charles | @OscarRandal-Williams Do you think you would be able to help me here, seeing as you developed the theory? | |
| Aug 4, 2018 at 21:29 | history | edited | Sergio Charles | CC BY-SA 4.0 |
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| Aug 4, 2018 at 21:15 | comment | added | Sergio Charles | Over $g$. @ArunDebray | |
| Aug 4, 2018 at 20:58 | comment | added | Arun Debray | What is the limit in your boxed question indexed over? | |
| Aug 4, 2018 at 19:49 | history | asked | Sergio Charles | CC BY-SA 4.0 |