The Homotopy Class of twisted $L_{\infty }$-morphisms

Abstract

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.

21 pages, comments are welcome! We would be happy to have suggestions about the literature

References in corpus (1)

• Erratum to: "A Proof of Tsygan's Formality Conjecture for an Arbitrary Smooth Manifold"