Timeline for Associated graded of a filtration of a tensor product
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 30, 2012 at 20:41 | comment | added | Vladimir Dotsenko | Glad you sorted it out! | |
| Aug 30, 2012 at 20:38 | vote | accept | Julian Kuelshammer | ||
| Aug 30, 2012 at 20:38 | comment | added | Julian Kuelshammer | The problem was more elementary, I got the definition of induced filtration wrong. Thanks for the help. | |
| Aug 30, 2012 at 16:10 | comment | added | Vladimir Dotsenko | Well, the induced filtration on the cobar-bar construction is naturally by the total number of tensor factors, $i_1+\ldots+i_k$ in the notation of your post, so I am puzzled by what worries you. $BA$ is a cofree coalgebra, so the differential of its cobar complex has a part coming from the differential of $BA$, and you seem to agree that after passing to the graded object this becomes the differential on $\overline{T^c(sA)}$ obtained by extending the differential of $A$, and a part coming from the (deconcatenation) coproduct on $BA$, it preserves the number of tensor factors and is unchanged. | |
| Aug 30, 2012 at 15:56 | comment | added | Julian Kuelshammer | If I understand you correctly, your answer is on the associated graded of $BA$, whose parts are $(SA)^{\otimes i}$. That I did understand, what I am missing is how this leads to the associated graded parts of $\Omega BA$. | |
| Aug 30, 2012 at 15:48 | history | answered | Vladimir Dotsenko | CC BY-SA 3.0 |