Tamarkin's proof of Kontsevich formality theorem

TL;DR

This paper provides a detailed explanation of Tamarkin's 1998 proof of the Kontsevich formality theorem, which establishes a deep connection between Hochschild cochains and deformation quantization.

Contribution

It clarifies and elaborates on Tamarkin's original proof, highlighting the role of homotopy Gerstenhaber algebra structures in Hochschild cochains.

Findings

Confirmed the existence of homotopy Gerstenhaber algebra structure in Hochschild cochains

Provided detailed steps of Tamarkin's proof of the formality theorem

Enhanced understanding of deformation quantization via formality

Abstract

In 1998 D. Tamarkin announced a proof of Kontsevich formality theorem based on the existence of structure of homotopy Gerstenhaber algebra in the Hochschild cochains of an associative algebra. In this note we give a detailed explanation of Tamarkin's result.