Timeline for A natural embedding of the total space of tautological bundle over $G(2,n)$ in $G(2,n+1)$
Current License: CC BY-SA 3.0
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
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| Nov 7, 2015 at 21:17 | vote | accept | Ali Taghavi | ||
| Oct 23, 2015 at 10:30 | answer | added | Liviu Nicolaescu | timeline score: 4 | |
| Oct 21, 2015 at 19:30 | answer | added | Sebastian Goette | timeline score: 2 | |
| Oct 21, 2015 at 14:57 | comment | added | Ali Taghavi | @SebastianGoette thanks.for your elegance argument using Thom isomorphism. | |
| Oct 21, 2015 at 8:46 | comment | added | Sebastian Goette | Regarding the cell structure obtained by gluing - it is not clear that you get the same as for $\mathbb C P^n$. But that does not matter if you are interested in homology only, because the resulting CW complex would only have cells in even dimensions. Then the cellular complex would have trivial differential, and hence be the same as for $\mathbb C P^n$ with the usual cell structure. | |
| Oct 21, 2015 at 7:58 | comment | added | Ali Taghavi | could you please more explain about cell structure and gluing cells? | |
| Oct 21, 2015 at 7:57 | answer | added | Achim Krause | timeline score: 5 | |
| Oct 21, 2015 at 7:49 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 21, 2015 at 7:32 | comment | added | Ali Taghavi | Moreover are we sure that these gluing maps induce the same maps as the $\mathbb{C}P^{n},s$( in relative homologies $H_{n}(X_{n+1}, X_{n})$)? | |
| Oct 21, 2015 at 7:26 | comment | added | Ali Taghavi | @SebastianGoette thank you very much for your very interesting comment. For such cell-gluing, are you considering the Thom space of the bundle? | |
| Oct 21, 2015 at 6:32 | comment | added | Sebastian Goette | You clearly cannot have a one-point remainder. Because if you had, then you would obtain $G(2,n+1)$ from $G(2,n)$ by gluing in a $2(n-1)$-cell. Inductively, $G(2,n)$ would have the same homology as $\mathbb C P^{n-2}$, but already $G(2,3)\cong\mathbb R P^2\not\cong\mathbb C P^1$. | |
| Oct 21, 2015 at 6:32 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 21, 2015 at 6:23 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 21, 2015 at 6:09 | history | edited | Ali Taghavi | CC BY-SA 3.0 |
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| Oct 21, 2015 at 5:54 | history | asked | Ali Taghavi | CC BY-SA 3.0 |