Contact homology and linearization without dga homotopies

TL;DR

This paper establishes that the set of linearized contact homologies for a closed contact manifold is a contact invariant, clarifying their status within the framework of contact dg-algebras.

Contribution

It proves that the isomorphism classes of linearized contact homologies are invariants of the contact structure, based on Pardon's foundations.

Findings

Linearized contact homologies form a contact invariant.

The set of isomorphism classes is well-defined under contactomorphisms.

Clarifies the relationship between contact homology and dg-algebra structures.

Abstract

This article clarifies the status of linearized contact homology given the foundations of the contact dg-algebra established by Pardon. In particular, we prove that the set of isomorphism classes of linearized contact homologies of a closed contact manifold is a contact invariant.