Timeline for Cohomology of configuration space of a compact manifold
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| S May 30, 2018 at 20:29 | history | suggested | Najib Idrissi |
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| May 30, 2018 at 20:23 | review | Suggested edits | |||
| S May 30, 2018 at 20:29 | |||||
| May 30, 2018 at 20:15 | answer | added | Najib Idrissi | timeline score: 4 | |
| Feb 24, 2013 at 9:57 | comment | added | Hicham Yamoul | I use the classical the following definition of ordered configuration space: Let $M$ an $m-$dimensional manifold. The space of ordered configurations of $k$ pointsis the space $$F(M,k)=\{(x_1,...,x_k)\in M^k ;x_i\neq x_j for i\neq j \}$$, and we ask to find the rational cohomology of this space. | |
| Feb 24, 2013 at 8:18 | comment | added | Dan Petersen | @Lee Mosher: here configuration space means $F(M,k) = M^k \setminus \Delta$ where $\Delta$ is the "big diagonal". | |
| Feb 24, 2013 at 8:06 | answer | added | Dan Petersen | timeline score: 2 | |
| Feb 24, 2013 at 5:14 | comment | added | Lee Mosher | Let me rephrase my question. What definition of a configuration space are you using? For example, is the space of k-element subsets of the 2-dimensional disc an example of your type of configuration space? The terminology "configuration space" is not completely standard, hence the need to state what definition you are using. | |
| Feb 23, 2013 at 22:05 | comment | added | Hicham Yamoul | I mean how to calculate the rational cohomology of the configuration space of a compact manifold simply connected in general, or if it is possible determinate a model fot the configuration space, i know that Kriz and Totaro gave a model for the configuration spaces $F(M,k)$ when $M$ is a complex projective manifold, but in general case, it is possible to use the same technics to determinate it? | |
| Feb 23, 2013 at 20:04 | comment | added | Lee Mosher | What kind of configuration spaces do you have in mind? For example, the configuration space of k points in the 2-dimensional disc is the classifying space of the k-strand braid group, and there is a rather large literature on its properties including its cohomology. Is that an example of what you are asking about? | |
| Feb 23, 2013 at 18:09 | history | asked | Hicham Yamoul | CC BY-SA 3.0 |