Following recent results of AK and VS on Z-graded manifolds, we give several local and
global normal forms results for Q-structures on those, ie for differential graded manifolds. In …

We prove that dg manifolds of finite positive amplitude, that is, bundles of positively graded
curved-algebras, form a category of fibrant objects. As a main step in the proof, we obtain a …

Generalized geometry finds many applications in the mathematical description of some
aspects of string theory. In a nutshell, it explores various structures on a generalized tangent …

In this paper we address several algebraic constructions in the context of groupoids,
algebroids and Z-graded manifolds. We generalize the results of integration of N-graded Lie …

Jet manifolds and vector bundles allow one to employ tools of differential geometry to study
differential equations, for example those arising as equations of motions in physics. They are …

We develop a new perspective on principal bundles with connection as morphisms from the
tangent bundle of the underlying manifold to a classifying dg-Lie groupoid. This groupoid …

We give a generalization of the theory of Z 2-graded manifolds to a theory of I-graded
manifolds, where I is a commutative semi-ring with some additional properties. We prove …

These lecture notes attempt to invite the reader towards the theory of singular foliations, both
smooth and holomorphic. In addition to a systematic review of the foundations, and an …

We develop the concept of a homogeneity supermanifold, which is more general than most
of the approaches to graded manifolds present in the literature. Instead of doing it via ringed …

For a Lie algebroid pair $ A\hookrightarrow L $ we study cocycles constructed from the
extension to $ L $ of the higher connection forms of a representation up to homotopy $ E $ of …