Timeline for $A_\infty$ structure on Ext-algebras well defined?
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2012 at 19:17 | comment | added | Leonid Positselski | Yes, I think one can: if X is an end-acyclic complex, P is a bounded above complex of projectives, and P -> X is a quasi-isomorphism, setting C to be the cone of the latter and arguing as above, one only needs the complexes Hom(P,C) and Hom(C,X) to be acyclic for the argument to hold. As H^*(Hom(P,P)) = H*(Hom(P,X)) = D(X,X[]) = Hot(X,X[]) = H^*(Hom(X,X)), this seems to be true. | |
| Mar 13, 2012 at 18:23 | vote | accept | Jan Weidner | ||
| Mar 13, 2012 at 18:23 | comment | added | Jan Weidner | Thank you for your explanation! Do you know, if one could take more generally instead of a projective/injective resolution an end-acyclic resolution in order to compute the $A_\infty$ structure? Here a complex X is called end-acyclic, if its shifted endomorphisms in the homotopy category and in the derived category coincide: Hot(X,X[n])=D(X,X[n]) for all n | |
| Mar 12, 2012 at 19:29 | history | edited | Leonid Positselski | CC BY-SA 3.0 |
fixed grammar ("of" and "the" inserted)
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| Mar 12, 2012 at 19:12 | history | answered | Leonid Positselski | CC BY-SA 3.0 |