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Torus actions on compact quotients

Anton Deitmar
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Abstract

We consider the action of a noncompact torus H on the compact quotient G/L, where G is a Lie group containing H and L is a uniform lattice in G. Using harmonic analysis on G we prove a formula relating the compact orbits of H to the action of H on the (infinite dimensional) tangential cohomology. The formula may be viewed as a Lefschetz formula or an equivariant index theorem for noncompact group actions.

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Anton Deitmar. 1996-06-24. Torus actions on compact quotients. https://arxiv.org/abs/dg-ga/9604008

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