  This is a survey article on a known generalization of Dirac-type operators to
transverse operators called basic Dirac operators on Riemannian foliations,
which are smooth foliations that have a transverse geometric structure.
Construction of these operators requires the additional structure of what is
called a bundle-like metric. We explain the result by Habib-R. that the
spectrum of such an operator is independent of the choice of bundle-like
metric, provided that the transverse geometric structure is fixed. We discuss
consequences, which include defining a new version of the exterior derivative
and de Rham cohomology that are nicely adapted to this transverse geometric
setting.
