Formal exponential map for graded manifolds

TL;DR

This paper introduces a formal exponential map for $Z$-graded manifolds, providing a new algebraic construction and extending classical theorems to this graded setting.

Contribution

It presents a purely algebraic formal exponential map for graded manifolds, enabling new resolutions and extending key theorems in the graded context.

Findings

Constructed a formal exponential map for $Z$-graded manifolds.

Provided a Fedosov type resolution of smooth functions on graded manifolds.

Extended the Emmrich--Weinstein theorem to $Z$-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.