Timeline for What is 'formal' ?
Current License: CC BY-SA 4.0
11 events
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| May 13, 2022 at 11:35 | comment | added | Aleksandar Milivojević | Regarding "In this language then, a dg algebra $(A,d)$ is formal if it is quasi-isomorphic, as an A-infinity algebra, to $H^*(A,d)$ with all higher products zero. In other words, all of the "Massey products" vanish*": the quasi-isomorphism used in the second DGMS quote is a map in the category of dga's, which is more restrictive than being a map of A-infinity algebras (even between dga's). So one needs here the additional (true) statement that two dga's are A-infinity-quasi-isomorphic iff they are dga-quasi-isomorphic. | |
| May 12, 2022 at 8:08 | history | edited | Glorfindel | CC BY-SA 4.0 |
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| Feb 13, 2017 at 10:18 | comment | added | Bruno Stonek | From what I've read, your "standard fact" was first proven by Kadeishvili and can be seen in some sources cited as "Kadeishvili's theorem". | |
| Aug 13, 2010 at 19:19 | comment | added | DamienC | "However, I believe that triviality of the A-infinity structure is equivalent to formality." This is true, if by "triviality" you mean that the transfered $A_\infty$-structure on cohomology is $A_\infty$-quasi-isomorphic (ie weakly equivalent) to the genuine agebra structure induced on cohomology. | |
| Mar 5, 2010 at 7:06 | vote | accept | Xiao Xinli | ||
| Feb 1, 2010 at 8:23 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Jan 26, 2010 at 19:05 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Jan 26, 2010 at 7:20 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Jan 26, 2010 at 7:09 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Jan 26, 2010 at 6:50 | history | edited | Kevin H. Lin | CC BY-SA 2.5 |
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| Jan 26, 2010 at 6:44 | history | answered | Kevin H. Lin | CC BY-SA 2.5 |