K-homology and index theory on contact manifolds

TL;DR

This paper addresses the index problem for a class of hypoelliptic Fredholm operators on closed contact manifolds, combining previous partial results with K-homology isomorphisms to provide a comprehensive solution.

Contribution

It provides a complete solution to the index problem for hypoelliptic operators on contact manifolds using K-homology techniques.

Findings

Solved the index problem for hypoelliptic operators on contact manifolds

Connected Van Erp's partial results with K-homology isomorphisms

Established a framework for analyzing hypoelliptic operators in contact geometry

Abstract

Let X be a closed connected contact manifold. On X there is a naturally arising class of hypoelliptic (but not elliptic) operators which are Fredholm. In this paper we solve the index problem for this class of operators. The solution is achieved by combining Van Erp's earlier partial result with the Baum-Douglas isomorphism of analytic and geometric K-homology.