Tensor products of homotopy Gerstenhaber algebras

TL;DR

This paper constructs a new algebraic structure called a Hirsch algebra on the tensor product of homotopy Gerstenhaber algebras, extending existing algebraic frameworks and applicable to related algebraic complexes.

Contribution

It introduces a novel Hirsch algebra structure on tensor products of homotopy Gerstenhaber algebras, broadening the scope of algebraic operations in homotopical algebra.

Findings

Hirsch algebra structure extends the canonical dg algebra structure

Applicable to tensor products of level 3 Hirsch algebras

Applicable to the Mayer-Vietoris double complex

Abstract

On the tensor product of two homotopy Gerstenhaber algebras we construct a Hirsch algebra structure which extends the canonical dg algebra structure. Our result applies more generally to tensor products of "level 3 Hirsch algebras" and also to the Mayer-Vietoris double complex.