Calabi–Yau structure on the Chekanov–Eliashberg algebra of a Legendrian sphere

Legout, Noémie

doi:10.2140/agt.2025.25.3627

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Calabi–Yau structure on the Chekanov–Eliashberg algebra of a Legendrian sphere

Noémie Legout

Algebraic & Geometric Topology 25 (2025) 3627–3677

DOI: 10.2140/agt.2025.25.3627

Abstract

We prove that the Chekanov–Eliashberg algebra of a horizontally displaceable $n$ -dimensional Legendrian sphere in the contactization of a Liouville manifold is an $(n + 1)$ -Calabi–Yau differential graded algebra. In particular it means that there is a quasi-isomorphism of DG bimodules between the diagonal bimodule and the inverse dualizing bimodule associated to the Chekanov–Eliashberg algebra. On some cyclic version of these bimodules, computing the Hochschild homology and cohomology of the Chekanov–Eliashberg algebra, we construct $A_{\infty}$ -operations and show that the Calabi–Yau isomorphism extends to a family of maps satisfying the $A_{\infty}$ -functor equations.

Keywords

Calabi–Yau structure, Chekanov–Eliashberg algebra, Rabinowitz Floer complex

Mathematical Subject Classification

Primary: 53D42, 57R58

References

Publication

Received: 24 August 2023

Revised: 28 May 2024

Accepted: 11 July 2024

Published: 1 October 2025

Authors

Noémie Legout
Department of Mathematical Sciences Chalmers University of Technology Göteborg Sweden

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Volume 25, issue 6 (2025)