Triviality of the higher formality theorem

Damien Calaque (1) , Thomas Willwacher (2)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 Institut für Mathematik [Zürich]

It is noted that the higher version of M. Kontsevich's Formality Theorem is much easier than the original one. Namely, we prove that the higher Hochschild-Kostant-Rosenberg map is already a homotopy e_{n+1}-formality quasi-isomorphism whenever n is at least 2.

Domaines: Algèbres quantiques [math.QA]

Damien Calaque, Thomas Willwacher. Triviality of the higher formality theorem. Proceedings of the American Mathematical Society, 2015, 143 (12), pp.5181-5193. ⟨10.1090/proc/12670⟩. ⟨hal-00904247⟩