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

Amorim, Lino; Tu, Junwu

doi:10.1090/tran/7321

Tensor product of cyclic $A_\infty$-algebras and their Kontsevich classes
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by Lino Amorim and Junwu Tu PDF

Trans. Amer. Math. Soc. 371 (2019), 1029-1061 Request permission

Abstract:

Given two cyclic $A_\infty$-algebras $A$ and $B$, in this paper 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.

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