On a compact contact manifold, a pseudodifferential operator in the Heisenberg calculus with an invertible symbol is a hypoelliptic Fredholm operator. The index theory of Heisenberg elliptic operators has been extensively investigated from various perspectives. In this talk, I will discuss a solution of the problem of finding a local formula for the index of such an operator as an expression in terms of the principal symbol of the operator and geometric data.
This is joint work with E. van Erp.