The deformation complex is a homotopy invariant of a homotopy algebra

TL;DR

This paper demonstrates that the deformation complex of a homotopy algebra remains invariant under homotopy equivalences, specifically showing that quasi-isomorphic homotopy algebras have quasi-isomorphic deformation complexes.

Contribution

It provides an explicit construction proving the deformation complex is a homotopy invariant under infinity quasi-isomorphisms of homotopy algebras.

Findings

Deformation complexes are invariant under homotopy equivalences.

Explicit construction of L-infinity quasi-isomorphisms between deformation complexes.

Homotopy invariance of the deformation complex established.

Abstract

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an explicit construction.