Stable Formality Quasi-isomorphisms for Hochschild Cochains I

Details Stable Formality Quasi-isomorphisms for Hochschild Cochains I Stable Formality Quasi-isomorphisms for Hochschild Cochains I

2011-09-27

arxiv.org/abs/1109.6031v1

Mathematics

K-Theory and Homology

The first version. Comments are welcome

Scientific paper

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".

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