higher geometry / derived geometry
Ingredients
Concepts
geometric little (∞,1)-toposes
geometric big (∞,1)-toposes
Constructions
Examples
derived smooth geometry
Theorems
∞-Lie theory (higher geometry)
Background
Smooth structure
Higher groupoids
Lie theory
∞-Lie groupoids
∞-Lie algebroids
Formal Lie groupoids
Cohomology
Homotopy
Related topics
Examples
$\infty$-Lie groupoids
$\infty$-Lie groups
$\infty$-Lie algebroids
$\infty$-Lie algebras
The notion of differential graded manifold is a generalization of the notion of smooth manifold from ordinary geometry to higher geometry, specifically to dg-geometry. Typically it is taken to be the formal dual to a dgc-algebra which in degree-0 is the algebra of? smooth functions on an ordinary smooth manifold.
Hence this is a graded manifold whose algebra of functions is equipped with a compatible differential.
Sometimes this is called an “NQ-supermanifold”.
An L-∞ algebroid over a smooth manifold may be thought of as a dg-manifold concentrated in non-negative degree.
A derived L-∞ algebroid may be thought of as a dg-manifold in arbitrary degree.
Last revised on October 5, 2017 at 10:07:42. See the history of this page for a list of all contributions to it.