The index of hypoelliptic operators on foliated manifolds

Abstract

In [vE1] and [vE2] we presented the solution to the index problem for a class of hypoelliptic operators on closed contact manifolds. The proofs are based on an adaptation of the tangent groupoid method of Alain Connes to hypoelliptic index problems. The methods originally developed for contact manifolds have wider applicability to the index theory of hypoelliptic Fredholm operators. As an illustration of the scope and effectiveness of these methods, we present here an index theorem for a class of hypoelliptic differential operators on closed foliated manifolds.