Chekanov-Eliashberg $\mathrm{dg}$-algebras for singular Legendrians

The Chekanov–Eliashberg $\mathrm{dg}$-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact manifold. We extend the definition to Legendrian embeddings of skeleta of Weinstein manifolds. Via Legendrian surgery, the new definition gives direct proofs of wrapped Floer cohomology push-out diagrams [22]. It also leads to a proof of a conjectured isomorphism [17, 25] between partially wrapped Floer cohomology and Chekanov–Eliashberg $\mathrm{dg}$-algebras with coefficients in chains on the based loop space.

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J.A. is supported by the Knut and Alice Wallenberg Foundation.

T.E. is supported by the Knut and Alice Wallenberg Foundation and the Swedish Research Council.

Received 9 February 2021

Received revised 14 June 2021

Accepted 16 September 2021

Published 28 February 2023