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arXiv · 2304.03014

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

Noémie Legout
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Abstract

In this paper, we prove that the Chekanov-Eliashberg algebra of an horizontally displaceable n-dimensional Legendrian sphere in the contactisation of a Liouville manifold is a (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, which are chain complexes 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.

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Noémie Legout. 2023-04-06. Calabi-Yau structure on the Chekanov-Eliashberg algebra of a Legendrian sphere. https://doi.org/10.2140/agt.2025.25.3627

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