Tensor product of cyclic 𝐴_{∞}-algebras and their Kontsevich classes

Abstract

Given two cyclic A ∞ A_\infty -algebras A A and B B , in this paper we prove that there exists a cyclic A ∞ A_\infty -algebra structure on their tensor product A ⊗ B A\otimes B which is unique up to a cyclic A ∞ A_\infty -quasi-isomorphism. Furthermore, the Kontsevich class of A ⊗ B A\otimes B is equal to the cup product of the Kontsevich classes of A A and B B on the moduli space of curves.