The transverse index theorem for proper cocompact actions of Lie groupoids

By Markus J. Pflaum, H. Posthuma, X. Tang. 2013

51 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f9681923d68b40a61d462256e06dd327825a3255