On Lagrangian cobordisms and the Chekanov-Eliashberg DGA

TL;DR

This paper studies how exact Lagrangian cobordisms induce maps on Chekanov-Eliashberg DGAs and their linearizations, proving invariance under isotopy and analyzing effects on algebraic structures.

Contribution

It adapts the DGA map to linearizations via augmentations and proves invariance of the induced maps on linearized contact homology and higher order structures.

Findings

The DGA map can be adapted to linearized contact homology.

Induced maps are invariant under Lagrangian isotopy.

Higher order product structures are preserved under the induced maps.

Abstract

In this paper, we consider exact Lagrangian cobordisms and the map they induce on the Chekanov-Eliashberg DGAs of their Legendrian ends as defined by Ekholm, Honda, and Kalman. Specifically, we show how to adapt this map to linearizations of the DGA using augmentations. We then show its induced map on linearized Legendrian contact homology is invariant under Lagrangian isotopy under mild hypotheses, as well as its induced map on higher order product structures.