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–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
References
Publication
Received: 15 June 2010
Accepted: 1 October 2010
Published: 6 January 2011
Authors
Constanze Roitzheim
Department of Mathematics
University of Glasgow
University Gardens
Glasgow
G12 8QW
UK
http://www.maths.gla.ac.uk/~croitzheim/
Sarah Whitehouse
School of Mathematics and Statistics
University of Sheffield
Hicks Building
Hounsfield Road
Sheffield S3 7RH
UK
http://www.sarah-whitehouse.staff.shef.ac.uk/