Tamarkins proof of Kontsevich formality theorem

Abstract

1.3. In the first part (Sections 2– 3) we review some basic facts on operads and Koszul operads. In Section 4 we study formality of algebras over a Koszul operad. Following Halperin-Stasheff [HS], we call a graded algebra H over a Koszul operad O intrinsically formal if any dg O-algebra with cohomology isomorphic to H is formal. We prove Theorem 4.1.3 which gives a sufficient condition of intrinsic formality of a graded algebra over a Koszul operad in terms of its cohomology.