Timeline for What is the relationship between spectral sequences and obstruction theory?
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 28, 2019 at 14:40 | vote | accept | Tim Campion | ||
| Apr 28, 2019 at 6:31 | comment | added | Denis Nardin | @TimCampion I guess if you want a pithy saying, obstruction theory is what happens at the border of a fringed spectral sequence (i.e. how you compute differentials in pointed sets). I wish I had something better to say about it, but I'm not aware of a general systematization of fringed spectral sequences, only examples of how to handle particular cases. And obstruction theory for non-principal Postnikov towers fits just fine in the framework, there's a reason I'm not asking $\mathcal{M}_{i+1}\to\mathcal{M}_i$ to be principal fibration. | |
| Apr 28, 2019 at 6:15 | history | edited | Denis Nardin | CC BY-SA 4.0 |
Typos everywhere + better explanation of Bousfield's work
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| Apr 28, 2019 at 1:08 | comment | added | Tim Campion | Thanks Denis, this is great, I will have to dig into Bousfield's paper! So I guess your perspective is that obstruction theory is the study of nice towers (although I suppose classical obstruction theory for non-principal Postnikov towers doesn't quite fit into your framework), and associated to any tower is a (fringed) Bousfield-Kan spectral sequence. So (fringed) spectral sequences actually look more general than obstruction theories in this sense -- I was kind of expecting the reverse! | |
| Apr 27, 2019 at 21:46 | history | edited | Denis Nardin | CC BY-SA 4.0 |
added 13 characters in body
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| Apr 27, 2019 at 21:39 | comment | added | Denis Nardin | All indices probably have off-by-one errors, so handle with care. | |
| Apr 27, 2019 at 21:38 | history | answered | Denis Nardin | CC BY-SA 4.0 |