Homology, Homotopy and Applications

Volume 26 (2024)

Number 1

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

Pages: 201 – 227

DOI: https://dx.doi.org/10.4310/HHA.2024.v26.n1.a14


Andreas Kraft (Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Germany)

Jonas Schnitzer (Mathematisches Institut, Albert-Ludwigs-Universität Freiburg, Germany)


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.


homotopy Lie algebra, deformation quantization

2010 Mathematics Subject Classification

16W60, 17B55, 53D55

Received 4 September 2022

Received revised 11 May 2023

Accepted 26 May 2023

Published 1 May 2024