Abstract
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.
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Acknowledgements
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.
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To Giovanni Felder on the occasion of his 50th birthday.
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Dolgushev, V., Tamarkin, D. & Tsygan, B. Formality Theorems for Hochschild Complexes and Their Applications. Lett Math Phys 90, 103–136 (2009). https://doi.org/10.1007/s11005-009-0350-3
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DOI: https://doi.org/10.1007/s11005-009-0350-3