nLab
Kähler-Dirac operator

Contents

Definition

For (X,g)(X,g) a Riemannian manifold, the exterior differential is a differential operator on (sections of the) exterior bundle. With respect to the induced inner product write d *d^\ast for its adjoint operator. The Kähler-Dirac operator is d+d *d + d^\ast.

Properties

The Kähler-Dirac operator defines a canonical K-homology class on XX.

Last revised on July 12, 2013 at 17:45:16. See the history of this page for a list of all contributions to it.