A brief bibliography on formality conjecture

This is an extremely brief and incomplete bibliography; an interested reader should most certainly add to it at least "the references therein".

Original papers:

• M. Kontsevich, "Deformation quantization of Poisson manifolds. I", arXiv:math/9709040.
• Kontsevich, Maxim, "Deformation quantization of Poisson manifolds". Lett. Math. Phys. 66 (2003), no. 3, 157--216.
• Dmitry E. Tamarkin, "Another proof of M. Kontsevich formality theorem", arXiv:math/9803025.
• Dmitry E. Tamarkin, "Formality of Chain Operad of Small Squares", arXiv:math/9809164.

Overviews and expositions:

• Keller, B. "Deformation quantization after Kontsevich and Tamarkin", in " Deformation, quantification, theorie de Lie", 19--62, Panorames et Syntheses, 20, Soc. Math. France, Paris, 2005.
  • A very good and clear introduction into the subject, does not assume any prior knowledge.
• Hinich, Vladimir, "Tamarkin's proof of Kontsevich formality theorem". Forum Math. 15 (2003), no. 4, 591--614 (also avaiable as arXiv:math/0003052).
  • A concise but clear exposition of Tamarkin's proof.

Further reading:

• Kontsevich, Maxim, "Deformation quantization of algebraic varieties". EuroConference Moshe Flato 2000, Part III (Dijon). Lett. Math. Phys. 56 (2001), no. 3, 271--294.
• Yekutieli, Amnon, "Deformation quantization in algebraic geometry". Adv. Math. 198 (2005), no. 1, 383--432.
• Van den Bergh, Michel, "On global deformation quantization in the algebraic case". J. Algebra 315 (2007), no. 1, 326--395.
• Dolgushev, Vasiliy; Tamarkin, Dmitry; Tsygan, Boris, "The homotopy Gerstenhaber algebra of Hochschild cochains of a regular algebra is formal". J. Noncommut. Geom. 1 (2007), no. 1, 1--25.
• Damien Calaque, Michel Van den Bergh, "Global formality at the $G_\infty$-level", arXiv:0710.4510, and "Hochschild cohomology and Atiyah classes", arXiv:0708.2725.