K-homology is the dual theory to K-theory. The Baum-Douglas (BD)
isomorphism of analytic and topological K-homology can be taken as
providing a framework within which the Atiyah-Singer index theorem can
be extended
to certain non-elliptic operators. This talk considers a class of
non-elliptic differential operators on compact contact manifolds.
These operators have been studied by a number of mathematicians.
Working within the BD framework,
the index problem will be solved for these operators. This is joint
work with Erik van Erp.