Compact Fukaya categories of general plumbings are generated by proper modules over associated Ginzburg dg algebras and equivalent to proper modules over wrapped Fukaya categories and to microlocal sheaves.
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Exact Lagrangian immersions with augmentations or bounding cochains are generated by Lagrangian cocores in Weinstein manifolds.
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Proper modules over Ginzburg dg algebras and compact Fukaya categories of plumbings
Compact Fukaya categories of general plumbings are generated by proper modules over associated Ginzburg dg algebras and equivalent to proper modules over wrapped Fukaya categories and to microlocal sheaves.
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Generation of immersed Lagrangians by cocores
Exact Lagrangian immersions with augmentations or bounding cochains are generated by Lagrangian cocores in Weinstein manifolds.