Uniqueness of $A_\infty$-structures and Hochschild cohomology

Details Uniqueness of $A_\infty$-structures and Hochschild cohomology Uniqueness of $A_\infty$-structures and Hochschild cohomology

2009-09-17

arxiv.org/abs/0909.3222v4

Mathematics

Algebraic Topology

The paper has been rearranged and the results are now formulated in terms of a filtration of the Hochschild cohomology groups.

Scientific paper

This paper investigates if a differential graded algebra can have more than one $A_\infty$-structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an $A_\infty$-structure up to quasi-isomorphism using Hochschild cohomology. We then extend this condition to Sagave's notion of derived $A_\infty$-algebras after introducing a notion of Hochschild cohomology that applies to this.

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