A simple construction of the Rumin algebra

TL;DR

This paper presents a straightforward and explicit method to construct the Rumin algebra on contact manifolds, simplifying the understanding of its structure as a contact invariant and its relation to de Rham cohomology.

Contribution

It introduces a new, simple construction of the Rumin algebra using Markl's Homotopy Transfer Theorem, making its properties more accessible.

Findings

The construction confirms the Rumin algebra as a contact invariant.

It explicitly relates the Rumin algebra to de Rham cohomology.

The method simplifies previous approaches to the Rumin algebra.

Abstract

The Rumin algebra of a contact manifold is a contact invariant $C_\infty$-algebra of differential forms which computes the de Rham cohomology algebra. We recover this fact by giving a simple and explicit construction of the Rumin algebra via Markl's formulation of the Homotopy Transfer Theorem.