Tensor product of filtered $A_{\infty }$-algebras

Abstract

We define the tensor product of filtered $A_{\infty }$-algebras. establish some of its properties and give a partial description of the space of bounding cochains in the tensor product. Furthermore we show that in the case of classical $A_{\infty }$-algebras our definition recovers the one given by Markl and Shnider. We also give a criterion that implies that a given $A_{\infty }$-algebra is quasi-isomorphic to the tensor product of two subalgebras. This will be used in a sequel to prove a Künneth Theorem for the Fukaya algebra of a product of Lagrangian submanifolds.

v2: Longer version of the paper to appear in Journal of Pure and Applied Algebra

References in corpus (1)

• The Künneth theorem for the Fukaya algebra of a product of Lagrangians

Cited by in corpus (5)

• Formulae in noncommutative Hodge theory
• Versality of the relative Fukaya category
• The Künneth theorem for the Fukaya algebra of a product of Lagrangians
• Tensor product of A${}_{\infty }$-categories
• The inverse function theorem for curved L-infinity spaces