#### Volume 11, issue 1 (2011)

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

### Constanze Roitzheim and Sarah Whitehouse

Algebraic & Geometric Topology 11 (2011) 107–143
##### Abstract

Working over a commutative ground ring, we establish a Hochschild cohomology criterion for uniqueness of derived ${A}_{\infty }$–algebra structures in the sense of Sagave. We deduce a Hochschild cohomology criterion for intrinsic formality of a differential graded algebra. This generalizes a classical result of Kadeishvili for the case of a graded algebra over a field.

##### Keywords
Hochschild cohomology, $A$–infinity algebra, formality
##### Mathematical Subject Classification 2000
Primary: 16E45
Secondary: 16E40, 55S30