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Costello's theorem,"open TCFT=Calabi Yau A-infinity category",he also mentions when applied to Fukaya category we can recover Gromov-Witten theory, but I see that it needs some assumption,also even if the assumption is true,I just see that the TCFT associated to Fukaya category is the same as the one associated to Gromov-Witten invariant, BUT can we from that TCFT to RECOVER Gromov-Witten invariants? (I mean the opposite direction) Because otherwise,it is not A model.

I appreciate if there is any answer.

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  • $\begingroup$ This is an open question. See arxiv.org/abs/math/0509264 and arxiv.org/abs/0806.0107 $\endgroup$
    – Kevin H. Lin
    Commented Jun 30, 2010 at 3:10
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    $\begingroup$ The answer to the question in the title is “no”. $\endgroup$
    – Harald Hanche-Olsen
    Commented Jun 30, 2010 at 3:37
  • $\begingroup$ If Costello's theorem is what you're interested in, section 4.2 of the Lurie(-Hopkins) article on the classification on TCFT's describes a generalization that may be better suited to deal with this. $\endgroup$
    – skupers
    Commented Jun 30, 2010 at 6:00
  • $\begingroup$ Kevin, do you read that paper"The Gromov-Witten potential associated to a TCFT", I have several questions? $\endgroup$
    – HYYY
    Commented Aug 20, 2010 at 10:27

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