Uniqueness of A∞–structures and Hochschild cohomology

Roitzheim, Constanze; Whitehouse, Sarah

doi:10.2140/agt.2011.11.107

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

Constanze Roitzheim and Sarah Whitehouse

Algebraic & Geometric Topology 11 (2011) 107–143

DOI: 10.2140/agt.2011.11.107

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

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/

Volume 11, issue 1 (2011)