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Is there any connection to CohFTs as defined by Witten in his 1988 paper (via topological twist) and the CohFTs as defined by Kontsevich and Manin (in the context of Gromov-Witten theory of course).

I mean, is there a general definition of CohFT such that every simple (physics or maths) example such as Donaldson theory, Vafa-Witten theory, Gromov-Witten theory, Donaldson-Thomas theory, etc falls under this definition?

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  • $\begingroup$ Are you ok with factorisation algebras? You can translate everything to this language. $\endgroup$ – user40276 Aug 29 '18 at 21:07
  • $\begingroup$ Can you please provide details? $\endgroup$ – Gorbz Aug 30 '18 at 7:26
  • $\begingroup$ I'm not the best person here to talk about factorisation algebras. For topological twists, you may want to look at arxiv.org/pdf/1805.10806.pdf . The point is that anything constructed from a BRST-BV like formalism will fit into this formalism too. But you want something less general I suppose. $\endgroup$ – user40276 Aug 31 '18 at 20:33
  • $\begingroup$ Btw, I think that Witten defined Gromov-Witten cohomologically before Kontsevich-Manin in intlpress.com/site/pub/files/_fulltext/journals/sdg/1990/0001/… $\endgroup$ – user40276 Aug 31 '18 at 20:38
  • $\begingroup$ Indeed, but unlike GW theory, Donaldson theory or Vafa-Witten theory do not fall under the same CohFT definition as the GW theory. Of course they live in different dimensions. But my question remains. Is there an umbrella definition for any CohFT for any dimension? $\endgroup$ – Gorbz Aug 31 '18 at 21:12

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