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Transactions of the American Mathematical Society

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


Authors: Lino Amorim and Junwu Tu
Journal: Trans. Amer. Math. Soc. 371 (2019), 1029-1061
MSC (2010): Primary 18G55; Secondary 57M15
DOI: https://doi.org/10.1090/tran/7321
Published electronically: July 31, 2018
MathSciNet review: 3885170
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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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Additional Information

Lino Amorim
Affiliation: Mathematical Institute, University of Oxford, Andrew Wiles Building, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, England
Email: camposamorim@maths.ox.ac.uk, lamorim@ksu.edu

Junwu Tu
Affiliation: Department of Mathematics, University of Missouri, Columbia, Missouri 65211
Email: tuju@missouri.edu

DOI: https://doi.org/10.1090/tran/7321
Received by editor(s): December 9, 2016
Received by editor(s) in revised form: April 3, 2017
Published electronically: July 31, 2018
Article copyright: © Copyright 2018 American Mathematical Society