iBet uBet web content aggregator. Adding the entire web to your favor.

Link to original content: http://ncatlab.org/nlab/show/graded manifold

graded manifold in nLab

nLab graded manifold

Contents

Context

Higher geometry

$\infty$ -Lie theory

Contents

Idea
Related concepts

Idea

Under the embedding of smooth manifolds into formal duals of R-algebras a smooth manifold $X$ is identified with the formal dual of its $\mathbb{R}$ -algebra of smooth functions. Given then a $\mathbb{Z}$ -graded module $\mathfrak{a}$ over $C^\infty(X)$ concentrated away from zero, the graded symmetric graded algebra

Sym_{C^\infty(X)}\left( \mathfrak{a} \right)

may naturally be thought of as the formal dual of a $\mathbb{Z}$ -graded manifold.

If moreover $Sym_{C^\infty(X)}\left(\mathfrak{a}\right)$ is equipped with a differential that makes it a differential graded-commutative algebra, then the formal dual is called a differential graded manifold.

Related concepts

Created on October 5, 2017 at 10:06:38. See the history of this page for a list of all contributions to it.