Timeline for 2-cells in the configuration space
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 11, 2014 at 5:50 | comment | added | user43326 | If you don't mind replacing the configuration space with another space which has the same homotopy type, there is also the "configuration complex" due to Jeff Smith. | |
| Oct 10, 2014 at 17:13 | comment | added | Reza Rezazadegan | Thank you very much Ricardo. You can write this as an answer as well. | |
| Oct 10, 2014 at 17:10 | history | edited | Reza Rezazadegan | CC BY-SA 3.0 |
minor edit
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| Oct 10, 2014 at 14:41 | comment | added | Ricardo Andrade | (continuation) Another important construction here is that of Salvetti complexes for complements of subspace arrangements. (2) Find cell structures on compactifications of configuration spaces: this is done for the one-point compactification of the space of configurations in the plane by Fox and Neuwirth in their article "Braid groups" (eudml.org/doc/165794). They use this to compute a presentation of the braid groups. (3) Inspired by Fox and Neuwirth, it is common nowadays to analyse "open-cell decompositions" or even more general stratifications of configuration spaces. | |
| Oct 10, 2014 at 14:41 | comment | added | Ricardo Andrade | CW structures on configuration spaces are often not very practical to study their homotopical properties, as there will be a lot of extraneous cells accounting for the essential non-compactness of the configuration space. In general, there are three common approaches in this direction. (1) Find cell complexes homotopy equivalent to the configuration spaces: see the book "Geometry and topology of configuration spaces" by Fadell and Husseini for descriptions of such CW-complexes. (to be continued...) | |
| Oct 10, 2014 at 13:14 | history | edited | Reza Rezazadegan | CC BY-SA 3.0 |
edited body
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| Oct 10, 2014 at 12:29 | history | asked | Reza Rezazadegan | CC BY-SA 3.0 |