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

Journal article, 2025

We prove that the Chekanov–Eliashberg algebra of a horizontally displaceable n-dimensional Legendrian sphere in the contactization of a Liouville manifold is an .nC1/-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 A1-operations and show that the Calabi–Yau isomorphism extends to a family of maps satisfying the A1-functor equations.