Chekanov–Eliashberg dg-algebras for singular Legendrians

The Chekanov–Eliashberg dg-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact mani-fold. 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 isomor-phism [17, 25] between partially wrapped Floer cohomology and Chekanov–Eliashberg dg-algebras with coefficients in chains on the based loop space.