Timeline for homotopy type of complement of subspace arrangement
Current License: CC BY-SA 2.5
6 events
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| Mar 21, 2010 at 12:17 | comment | added | student | Hi,algori.Thank you for your answer.I am eager to get a clear picture of the solution.would you please talk about some details. ---student | |
| Mar 21, 2010 at 0:37 | comment | added | Tom Church | Since you were talking about $M$, I had taken $p$ as being defined from $T^4\to T^2$, rather than from $T^4\setminus \bar{M}\to T^2$. Now it seems clear that you meant the latter, so I withdraw my objection. | |
| Mar 21, 2010 at 0:09 | comment | added | algori | Tom, thanks, I misread the question and used $M$ for the complement. This has been fixed. Re "the preimage $p^{−1}(W)$ has cohomology in dimension 3": why? | |
| Mar 21, 2010 at 0:02 | history | edited | algori | CC BY-SA 2.5 |
corrected the notation
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| Mar 20, 2010 at 23:50 | comment | added | Tom Church | It is $M_1$, etc. that is homotopy equivalent to $p^{-1}(W)$, not all of $M$. Also, the preimage $p^{-1}(W)$ has cohomology in dimension 3, so cannot be homotopy equivalent to $X$ or any 2-complex. Anyway, the question is about the complement of $M$, not $M$ itself. For $M$, you can apply Gromov's CAT(1) link condition to see that $M$ is locally CAT(0), and thus aspherical. | |
| Mar 20, 2010 at 22:58 | history | answered | algori | CC BY-SA 2.5 |