The Homotopy Braces Formality Morphism
Abstract
We extend M. Kontsevich's formality morphism to a homotopy braces morphism and to a homotopy Gerstenhaber morphism. We show that this morphism is homotopic to D. Tamarkin's formality morphism, obtained using formality of the little disks operad, if in the latter construction one uses the Alekseev-Torossian associator. Similar statements can also be shown in the "chains" case, i.e., on Hochschild homology instead of cohomology. This settles two well known and long standing problems in deformation quantization and unifies the several known graphical constructions of formality morphisms and homotopies by Kontsevich, Shoikhet, Calaque, Rossi, Alm, Cattaneo, Felder and the author.
Cite
@article{arxiv.1109.3520,
title = {The Homotopy Braces Formality Morphism},
author = {Thomas Willwacher},
journal= {arXiv preprint arXiv:1109.3520},
year = {2016}
}
Comments
The title was changed in the publication process. The old title was "A Note on Br-infinity and KS-infinity formality". The article will appear under the current title in the Duke Math. Journal