The homotopy class of twisted $L_\infty$-morphisms

The global formality of Dolgushev depends on the choice of a torsion-free covariant derivative. We prove that the globalized formalities with respect to two different covariant derivatives are homotopic. More explicitly, we derive the statement by proving a more general homotopy equivalence between $L_\infty$-morphisms that are twisted with gauge equivalent Maurer–Cartan elements.

Keywords

homotopy Lie algebra, deformation quantization

2010 Mathematics Subject Classification

16W60, 17B55, 53D55

The full text of this article is unavailable through your IP address: 18.117.72.24

Received 4 September 2022

Received revised 11 May 2023

Accepted 26 May 2023

Published 1 May 2024