The equivariant index theorem for
transversally elliptic operators and the basic index theorem for Riemannian
Jochen Brüning - Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099 Berlin, Germany (email)
Abstract: In this expository paper, we explain a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a $G$-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications is an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.
Keywords: Equivariant, index, transversally elliptic, eta invariant,
Received: August 2010; Revised: October 2010; Available Online: December 2010.