The transverse index theorem for proper cocompact actions of Lie groupoids
Differential Geometry
2014-06-06 v2 K-Theory and Homology
Quantum Algebra
Abstract
Given a proper, cocompact action of a Lie groupoid, we define a higher index pairing between invariant elliptic differential operators and smooth groupoid cohomology classes. We prove a cohomological index formula for this pairing by applying the van Est map and algebraic index theory. Finally we discuss in examples the meaning of the index pairing and our index formula.
Keywords
Cite
@article{arxiv.1301.0479,
title = {The transverse index theorem for proper cocompact actions of Lie groupoids},
author = {M. J. Pflaum and H. Posthuma and X. Tang},
journal= {arXiv preprint arXiv:1301.0479},
year = {2014}
}
Comments
29 pages