English

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 AA_\infty-structure extending the given differential graded algebra structure. We give a sufficient condition for uniqueness of such an AA_\infty-structure up to quasi-isomorphism using Hochschild cohomology. We then extend this condition to Sagave's notion of derived AA_\infty-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