Formal exponential map for graded manifolds

Abstract

We introduce, for every $\mathbb{Z}$-graded manifold, a formal exponential map defined in a purely algebraic way and study its properties. As an application, we give a simple new construction of a Fedosov type resolution of the algebra of smooth functions of $\mathbb{Z}$-graded manifolds and we extend the Emmrich--Weinstein theorem to the context of $\mathbb{Z}$-graded manifolds.

24 pages

References in corpus (1)

• The Atiyah class of a dg-vector bundle

Cited by in corpus (7)

• Globalization for Perturbative Quantization of Nonlinear Split AKSZ Sigma Models on Manifolds with Boundary
• Dg manifolds, formal exponential maps and homotopy Lie algebras
• Hochschild cohomology of dg manifolds associated to integrable distributions
• Fedosov dg manifolds associated with Lie pairs
• Hopf algebras arising from dg manifolds
• $A_{\infty }$-Algebras from Lie Pairs
• Quantization of (-1)-Shifted Derived Poisson Manifolds