Timeline for Local homology of a space of unitary matrices
Current License: CC BY-SA 3.0
18 events
| when toggle format | what | by | license | comment | |
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| May 11, 2017 at 23:00 | vote | accept | John Klein | ||
| May 11, 2017 at 22:06 | history | bounty ended | John Klein | ||
| May 8, 2017 at 12:32 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 8, 2017 at 12:08 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 7, 2017 at 1:42 | vote | accept | John Klein | ||
| May 11, 2017 at 22:06 | |||||
| May 6, 2017 at 13:23 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 6, 2017 at 12:46 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 6, 2017 at 12:41 | comment | added | Gregory Arone | I added something about the general case to the answer. | |
| May 6, 2017 at 12:40 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 5, 2017 at 23:43 | comment | added | John Klein | I have to work through this, but I think your argument seems to be correct. | |
| May 5, 2017 at 23:27 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 5, 2017 at 23:11 | comment | added | Gregory Arone | Suppose $g$ fixes a subspace of dimension $k$ in ${\mathbb C}^n$. Then a small open neighborhood of $g$ in $\mathcal D$ is homeomorphic to a vector bundle of dimension $n^2-k^2$ over an open neighborhood of the identity in ${\mathcal D}_k\subset U(k)$. I think it follows that the local homology of $\mathcal D$ at $g$ is isomorphic to the local homology of ${\mathcal D}_k$ at the identity shifted up by $n^2-k^2$, essentially by a Thom isomorphism. | |
| May 5, 2017 at 22:31 | comment | added | John Klein | Greg, I should have said that knew how to do that case already. I am pretty certain that that the argument for $g \ne I$ is going to be more complicated because the stratification is different at different points of $\cal D$. What idea do you you have in mind to reduce the general case to the one in your post? I think that may be the crux of the matter! | |
| May 5, 2017 at 22:22 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 5, 2017 at 22:13 | history | edited | Gregory Arone | CC BY-SA 3.0 |
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| May 5, 2017 at 22:10 | history | undeleted | Gregory Arone | ||
| May 5, 2017 at 22:05 | history | deleted | Gregory Arone | via Vote | |
| May 5, 2017 at 21:59 | history | answered | Gregory Arone | CC BY-SA 3.0 |