Timeline for Does a filtered A_N algebra give rise to a multiplicative spectral sequence?
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 27, 2018 at 23:24 | vote | accept | algebrachallenged | ||
| Jan 27, 2018 at 22:36 | answer | added | John Rognes | timeline score: 2 | |
| Jan 26, 2018 at 12:49 | comment | added | algebrachallenged | P.S. I gather examples that you are asking about can be constructed using homotopy theory by taking suitable versions of chains on spaces considered here: mathoverflow.net/questions/248416/… and equipping them with a Pontryagin product. | |
| Jan 26, 2018 at 12:44 | comment | added | algebrachallenged | Perhaps I was not sufficiently clear in my explanation since I thought it was a standard definition. I am assuming that operations of arity N+1 and higher are not defined. So (with suitable sign conventions) for N=3, I would have m_1 is a differential (Eq. 1), m_2 satisfies Leibnitz rule (Eq. 2), multiplication is associative up to a homotopy m_3 (Eq. 3). This seems like a very natural structure. Examples typically extend to $A_\infty$ structure, however that extension may require some extra work. The question is whether that work is needed for constructing a mult. spectral seq. | |
| Jan 26, 2018 at 11:47 | comment | added | Vladimir Dotsenko | Are you sure in your definition of $A_N$-algebras to only have the $A_\infty$-equations for $i\le N$? I mean, a natural way to truncate $A_\infty$ is to say that operations of arity greater than $N$ vanish, but that would give equations for $i\le 2N-1$. Do you have any meaningful examples of your $A_N$-algebras where the equations from $N+1$ to $2N-1$ do not hold? | |
| Jan 26, 2018 at 11:44 | comment | added | Pedro | It seems to me this should follow from the fact that the filtering condition for $A_\infty$-algebras is simply the condition that the coderivation $b : BA\to BA$ on the bar construction on $A$ preserves the induced filtration on $BA$. Then all your known formalism works. | |
| Jan 26, 2018 at 10:39 | history | edited | algebrachallenged | CC BY-SA 3.0 |
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| Jan 25, 2018 at 18:25 | review | First posts | |||
| Jan 25, 2018 at 18:38 | |||||
| Jan 25, 2018 at 18:21 | history | asked | algebrachallenged | CC BY-SA 3.0 |