{"paper":{"title":"Uniqueness of $A_\\infty$-structures and Hochschild cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Constanze Roitzheim, Sarah Whitehouse","submitted_at":"2009-09-17T13:54:03Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0909.3222","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}