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

Full Text (PDF format)

Received 4 September 2022

Received revised 11 May 2023

Accepted 26 May 2023

Published 1 May 2024