Uniqueness of $A_\infty$-structures and Hochschild cohomology
Algebraic Topology
2014-10-01 v4
Abstract
This paper investigates if a differential graded algebra can have more than one -structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an -structure up to quasi-isomorphism using Hochschild cohomology. We then extend this condition to Sagave's notion of derived -algebras after introducing a notion of Hochschild cohomology that applies to this.
Keywords
Cite
@article{arxiv.0909.3222,
title = {Uniqueness of $A_\infty$-structures and Hochschild cohomology},
author = {Constanze Roitzheim and Sarah Whitehouse},
journal= {arXiv preprint arXiv:0909.3222},
year = {2014}
}
Comments
The paper has been rearranged and the results are now formulated in terms of a filtration of the Hochschild cohomology groups. To appear in Algebraic and Geometric Topology