English

Singular Legendrian unknot links and relative Ginzburg algebras

Symplectic Geometry 2025-10-15 v2 Geometric Topology Representation Theory

Abstract

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

Keywords

Cite

@article{arxiv.2311.03330,
  title  = {Singular Legendrian unknot links and relative Ginzburg algebras},
  author = {Johan Asplund},
  journal= {arXiv preprint arXiv:2311.03330},
  year   = {2025}
}

Comments

15 pages, 9 figures. v2: Final version. Comments welcome