Timeline for Multiplicative structure on spectral sequence
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Feb 9, 2016 at 15:08 | comment | added | Sean Tilson | I don't think that there is a mistake. Usually one wants to not have to check conditions on the level of the exact couple. Also, most spectral sequences that topologists care about don't come from filtered DGAs but from filtered spaces or filtered spectra. It might then take a great deal of care to show that one can obtain a filtered DGA from that set up , or a filtered $E_{\infty}$-DGA. I looked up ams.org/journals/tran/1973-177-00/S0002-9947-1973-0372860-2/… and they don't seem to mention the Massey article at all. | |
| Feb 9, 2016 at 14:59 | comment | added | Sebastian Goette | @SeanTilson You are a bit too pessimistic about Massey's paper. Please have a look at section 7, where he discusses filtered rings. The conditions there look as if they were easy enough to verify in special cases. What worries me however, is the age of this paper compared to problems in more recent books (Ravenel, and Hatcher's tentative fifth chapter) that deal with multiplicative spectral sequences. Did anybody discover a mistake in Massey's article? | |
| Feb 9, 2016 at 13:23 | comment | added | Sean Tilson | A similarly useful statement is the following. Given a symmetric monoidal model category M (with probably lots of other adjectives like stable and suitably enriched) filtered objects inherit a monoidal structure such that monoids with respect to that structure have associated spectral sequences that are multiplicative. | |
| Feb 9, 2016 at 13:19 | comment | added | Sergei Ivanov | Generally, I agree. A useful statement is that a filtered dg-algebra gives a multiplicative spectral sequence. | |
| Feb 9, 2016 at 13:11 | comment | added | Sean Tilson | This paper, as I recall, essentially boils down to "a spectral sequence is multiplicative iff it is multiplicative". I don't think that the conditions here are helpful. | |
| Feb 9, 2016 at 12:45 | history | answered | Sergei Ivanov | CC BY-SA 3.0 |