Tensor product of cyclic $A_\infty$-algebras and their Kontsevich classes
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- by Lino Amorim and Junwu Tu PDF
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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.References
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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
- MR Author ID: 986254
- 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
- Received by editor(s): December 9, 2016
- Received by editor(s) in revised form: April 3, 2017
- Published electronically: July 31, 2018
- © Copyright 2018 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 371 (2019), 1029-1061
- MSC (2010): Primary 18G55; Secondary 57M15
- DOI: https://doi.org/10.1090/tran/7321
- MathSciNet review: 3885170