Timeline for Natural transformation of $A_\infty$-functors lifted from homology
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Mar 8, 2019 at 19:35 | comment | added | Mohammed Abouzaid | The answer is negative, and you can find an obstruction theory for such problems discussed in Seidel's book. For an example, try $A = C^*(S^2)$ and $B= C^*(S^3)$, and $F$ and $G$ respectively given by the Hopf map and the trivial map. | |
| Mar 8, 2019 at 18:38 | comment | added | Vincent L. | Hi Alec! I mean, existence would already be good news but in the end I'm interested in knowing about some structure being preserved by functors between different instances of the Fukaya category and I dont think I would be able to SEE that from just knowing the natural transformation exists | |
| Mar 8, 2019 at 18:06 | comment | added | Alec Rhea | Interesting question and welcome to MO Vincent — out of curiosity, what would an explicit construction give you that existence wouldn’t (aside from the obvious advantage of a better understanding of the machinery in play, but in the context of proving something further is there an advantage)? | |
| Mar 8, 2019 at 17:30 | review | First posts | |||
| Mar 8, 2019 at 17:31 | |||||
| Mar 8, 2019 at 17:29 | history | asked | Vincent L. | CC BY-SA 4.0 |