Timeline for Why we have to fix markers in SFT?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2010 at 18:00 | comment | added | Tim Perutz | OK, thanks for pushing me to make this clear. The definition of the contact homology differential (e.g. as in B-O section 3) involves not just cylinders, but compactified spaces of rational curves with multiple punctures, each with an asymptotic marker. I believe that the SFT compactification is not quite the same as "D-M space with asymptotic markers", so forgetting markers would radically change the spaces. So far as I can see, the index and orientation (or bad orbit) issues are not particularly relevant here. | |
| Apr 20, 2010 at 17:25 | comment | added | Mohammad Farajzadeh-Tehrani | I agree that it makes some differences. But what will happen if we forget the marking? Does it make problem for : -orienting moduli space -compactifying moduli space -defining CZ index ? | |
| Apr 20, 2010 at 16:42 | comment | added | Tim Perutz | The differences become apparent when one looks at the compactified moduli spaces. For a visualization, see Bourgeois-Oancea, arxiv.org/abs/0704.2169 section 6 (p. 39 in the linked ArXiv version). | |
| Apr 20, 2010 at 15:54 | comment | added | Mohammad Farajzadeh-Tehrani | Look at last paragraph of page 4 of "Coherent orientations in..." | |
| Apr 20, 2010 at 15:52 | comment | added | Mohammad Farajzadeh-Tehrani | I don't think that this the reason. If there is a reason, that should be hided in the orientation problem, or definition of CZ index. None of the things you said force us to put markers, and in all cases you can simply consider moduli spaces which asymptote to Reeb orbits. | |
| Apr 20, 2010 at 15:06 | history | answered | Tim Perutz | CC BY-SA 2.5 |