The Atiyah-Singer index formula for subelliptic operators on contact manifolds. Part II
成果类型：
Article
署名作者：
van Erp, Erik
刊物名称：
ANNALS OF MATHEMATICS
ISSN/ISSBN：
0003-486X
发表日期：
2010
页码：
1683-1706
关键词：
摘要：
We present a new solution to the index problem for hypoelliptic operators in the Heisenberg calculus on contact manifolds, by constructing the appropriate topological K-theory cocycle for such operators. Its Chern character gives a cohomology class to which the Atiyah-Singer index formula can be applied. Such a K- cocycle has already been constructed by Boutet de Monvel for Toeplitz operators, and, more recently, by Melrose and Epstein for the class of Hermite operators. Our construction applies to general hypoelliptic pseudodifferential operators in the Heisenberg calculus. As in the Hermite Index Formula of Melrose and Epstein, our construction gives a vector bundle automorphism of the symmetric tensors of the contact hyperplane bundle. This automorphism is constructed directly from the invertible Heisenberg symbol of the operator, and is easily computed in the case of differential operators.