Singular Legendrian unknot links and relative Ginzburg algebras

Asplund, Johan

doi:10.2140/agt.2025.25.3737

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Singular Legendrian unknot links and relative Ginzburg algebras

Johan Asplund

Algebraic & Geometric Topology 25 (2025) 3737–3754

DOI: 10.2140/agt.2025.25.3737

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 $Λ$ . We prove that the relative Ginzburg algebra of $(Q, F)$ is quasi-isomorphic to the Chekanov–Eliashberg dg-algebra of $Λ$ . It follows that the Chekanov–Eliashberg dg-algebra of $Λ$ 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.

Keywords

Chekanov–Eliashberg algebra, relative Ginzburg algebra, Calabi–Yau structure

Mathematical Subject Classification

Primary: 53D35, 53D42

Secondary: 16E45

References

Publication

Received: 6 November 2023

Revised: 15 May 2024

Accepted: 1 June 2024

Published: 1 October 2025

Authors

Johan Asplund
Department of Mathematics Stony Brook University Stony Brook, NY United States

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Volume 25, issue 6 (2025)