Exact Lagrangian immersions carrying positive-action bounding cochains - equivalently augmentations of their Legendrian lifts' Chekanov-Eliashberg algebras - are generated by the Lagrangian cocores of the ambient Weinstein manifold.
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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.
Reduced loop homology is introduced so the loop product and coproduct form a unital infinitesimal anti-symmetric bialgebra satisfying a modified Sullivan relation, established via reduced symplectic homology on Weinstein manifolds.
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Generation of immersed Lagrangians by cocores
Exact Lagrangian immersions carrying positive-action bounding cochains - equivalently augmentations of their Legendrian lifts' Chekanov-Eliashberg algebras - are generated by the Lagrangian cocores of the ambient Weinstein manifold.
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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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Reduced symplectic homology and string topology
Reduced loop homology is introduced so the loop product and coproduct form a unital infinitesimal anti-symmetric bialgebra satisfying a modified Sullivan relation, established via reduced symplectic homology on Weinstein manifolds.