There appears to be a dearth of resources and references for the question of 'locality' in Floer theory. In particular, I cannot seem to find any complete statement of what people refer to as 'Kontsevich's cosheaf conjecture' or why the work of Ganatra-Pardon-Shende ('18) resolves this conjecture (partially or wholly). I would appreciate a direction to a reference of Kontsevich's conjecture (if one exists) or a sketch of its formulation. Furthermore, I would appreciate if someone could link this statement directly to the work of Ganatra-Pardon-Shende.
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1$\begingroup$ My answer here might interest you: mathoverflow.net/questions/11273/… You should also check out Kontsevich's paper on this ("Symplectic geometry of homological algebra"). The conjecture states that the Fukaya category of a Weinstein manifold is quasi-isomorphic to the category of microlocal sheaves on the skeleton. $\endgroup$– Jonny EvansCommented May 2, 2019 at 21:09
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$\begingroup$ I think there are multiple things which people mean when they refer to locality in Floer theory. Some people (e.g. Verbitsky, I believe) refer to the lack of instanton (i.e. pseudoholomorphic curve) corrections for Floer groups of holomorphic Lagrangians in hyperkaehler manifolds. Most people refer to Kontsevich cosheaf conjecture towards which Pardon and other people are making progress. The third is locality in Seidel's sense, which can be confused with locality in Kontsevich's sense but is logically distinct from it. I think this is explained by Dr. Shende in the link above. $\endgroup$– user138661Commented May 3, 2019 at 9:01
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$\begingroup$ Maybe there are some other senses too, this is a vast topic and I gave up on ever understanding it completely. $\endgroup$– user138661Commented May 3, 2019 at 9:01
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