Letters in Mathematical Physics

, Volume 90, Issue 1–3, pp 103–136 | Cite as

Formality Theorems for Hochschild Complexes and Their Applications

  • Vasiliy Dolgushev
  • Dmitry Tamarkin
  • Boris Tsygan
Open Access


We give a popular introduction to formality theorems for Hochschild complexes and their applications. We review some of the recent results and prove that the truncated Hochschild cochain complex of a polynomial algebra is non-formal.

Mathematics Subject Classification (2000)

19D55 53D55 


Hochschild complexes deformation quantization 



We would like to thank J. Stasheff for discussions and for his useful comments on the first version of our manuscript. D.T. and B.T. are supported by NSF grants. The work of V.D. is partially supported by the Grant for Support of Scientific Schools NSh-3036.2008.2.

Open Access

This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.


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Copyright information

© The Author(s) 2009

Authors and Affiliations

  • Vasiliy Dolgushev
    • 1
  • Dmitry Tamarkin
    • 2
  • Boris Tsygan
    • 2
  1. 1.Department of MathematicsUniversity of California at RiversideRiversideUSA
  2. 2.Mathematics DepartmentNorthwestern UniversityEvanstonUSA

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