nLab Kähler-Dirac operator

Definition

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

Properties

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

Related concepts

• Dolbeault-Dirac operator

• Spin^c Dirac operator