Stable Formality Quasi-isomorphisms for Hochschild Cochains
Abstract
We consider L-infinity quasi-isomorphisms for Hochschild cochains whose structure maps admit "graphical expansion". We introduce the notion of stable formality quasi-isomorphism which formalizes such an L-infinity quasi-isomorphism. We define a homotopy equivalence on the set of stable formality quasi-isomorphisms and prove that the set of homotopy classes of stable formality quasi-isomorphisms form a torsor for the group corresponding to the zeroth cohomology of the full (directed) graph complex. This result may be interpreted as a complete description of homotopy classes of formality quasi-isomorphisms for Hochschild cochains in the "stable setting".
Cite
@article{arxiv.1109.6031,
title = {Stable Formality Quasi-isomorphisms for Hochschild Cochains},
author = {Vasily Dolgushev},
journal= {arXiv preprint arXiv:1109.6031},
year = {2019}
}
Comments
The final version will appear in M\'emoires de la Soci\'et\'e Math\'ematique de France (N.S.)