Tensor product of cyclic A${}_{\infty }$-algebras and their Kontsevich classes

Abstract

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

arXiv commentv2: One mistake fixed, expanded discussion of odd inner products

References in corpus (1)

• Tensor Products of $A_{\infty }$-algebras with Homotopy Inner Products