The eta invariant and equivariant index of transversally elliptic operators

Details The eta invariant and equivariant index of transversally elliptic operators The eta invariant and equivariant index of transversally elliptic operators

2010-05-20

arxiv.org/abs/1005.3845v2

Mathematics

Differential Geometry

62 pages, typos corrected

Scientific paper

We prove 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, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

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