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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Modified c- and g-vectors of the Markov quiver exhibit a fractal structure via linear isomorphisms and admit recursive formulas parameterized by coprime integers, which classify the complement of the G-fan.
Exact Lagrangian immersions with augmentations or bounding cochains are generated by Lagrangian cocores in Weinstein manifolds.
The authors prove that proper relative Ginzburg algebras yield an additive Λ-cluster algebra structure via negative extensions in Higgs categories, providing an additive view of the monoidal Λ-invariant for untwisted simply-laced types.
citing papers explorer
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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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Fractal phenomenon in $c$- and $g$-vectors of the Markov quiver
Modified c- and g-vectors of the Markov quiver exhibit a fractal structure via linear isomorphisms and admit recursive formulas parameterized by coprime integers, which classify the complement of the G-fan.
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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.
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Additive categorification of the monoidal $\Lambda$-invariant
The authors prove that proper relative Ginzburg algebras yield an additive Λ-cluster algebra structure via negative extensions in Higgs categories, providing an additive view of the monoidal Λ-invariant for untwisted simply-laced types.