Abstract
Recently the first two authors (Cattaneo and Felder in 2008) constructed an L ∞-morphism using the S 1-equivariant version of the Poisson Sigma Model. Its role in the deformation quantization was not entirely clear. We give here a “good” interpretation and show that the resulting formality statement is equivalent to formality on cyclic chains as conjectured by Tsygan and proved recently by several authors (Dolgushev et al. in 2008; Willwacher in 2008).
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This work has been partially supported by SNF Grants 200020-121640/1 and 200020-105450, by the European Union through the FP6 Marie Curie RTN ENIGMA (contract number MRTN-CT-2004-5652), and by the European Science Foundation through the MISGAM program.
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Sergio Cattaneo, A., Felder, G. & Willwacher, T. On L ∞-Morphisms of Cyclic Chains. Lett Math Phys 90, 85–101 (2009). https://doi.org/10.1007/s11005-009-0338-z
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DOI: https://doi.org/10.1007/s11005-009-0338-z