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arXiv · 1311.4073

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

Lino Amorim·Junwu Tu
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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.

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Lino Amorim, Junwu Tu. 2013-11-16. Tensor product of cyclic A$_\infty$-algebras and their Kontsevich classes. https://arxiv.org/abs/1311.4073

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