Journal of Symplectic Geometry

Volume 20 (2022)

Number 3

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

Pages: 509 – 559

DOI: https://dx.doi.org/10.4310/JSG.2022.v20.n3.a1

Authors

Johan Asplund (Department of Mathematics, Uppsala University, Uppsala, Sweden)

Tobias Ekholm (Department of Mathematics, Uppsala University, Uppsala, Sweden; and Institut Mittag-Leffler, Djursholm, Sweden)

Abstract

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.

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