Singular Legendrian unknot links and relative Ginzburg algebras

Abstract

We associate to a quiver and a subquiver $(Q,F)$ a stopped Weinstein manifold $X$ whose Legendrian attaching link is a singular Legendrian unknot link $\Lambda$. We prove that the relative Ginzburg algebra of $(Q,F)$ is quasi-isomorphic to the Chekanov--Eliashberg dg-algebra of $\Lambda$. It follows that the Chekanov--Eliashberg dg-algebra of $\Lambda$ relative to its boundary dg-subalgebra, and the Orlov functor associated to the partially wrapped Fukaya category of $X$ both admit a strong relative smooth Calabi--Yau structure.

arXiv comment15 pages, 9 figures. v2: Final version. Comments welcome

References in corpus (11)

• Covariantly functorial wrapped Floer theory on Liouville sectors
• Duality between Lagrangian and Legendrian invariants
• Relative Calabi-Yau structures
• On partially wrapped Fukaya categories
• Augmentations are Sheaves
• Cyclic homology, $S^1$-equivariant Floer cohomology, and Calabi-Yau structures
• Relative critical loci and quiver moduli
• Chekanov-Eliashberg dg-algebras for singular Legendrians
• Koszul duality via suspending Lefschetz fibrations
• A Chekanov-Eliashberg algebra for Legendrian graphs
• Tangle contact homology

Cited by in corpus (1)

• Persistence of unknottedness of clean Lagrangian intersections