For a Riemannian manifold $M$, a Clifford module is a bundle over $M$ that is, fiberwise, a representation of the Clifford algebra bundle $\mathrm{Cl}(TM)$ and has a connection compatible with this action. The canonical examples of Clifford modules are

- $\Lambda^* M$ (in two ways, with the grading formed by the degree of differential forms or with the hodge star).
- The spinor bundle associated to a spin or spin$^c$ structure.
- The Dolbeault complex $\Lambda^{0,*} TM$ for a complex manifold (which is really a special case of a spin$^c$ structure).

Are there other examples of Clifford modules that come up naturally?