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Integration over homogeneous spaces for classical Lie groups using iterated residues at infinity

Magdalena Zielenkiewicz (2014)

Open Mathematics

Using the Berline-Vergne integration formula for equivariant cohomology for torus actions, we prove that integrals over Grassmannians (classical, Lagrangian or orthogonal ones) of characteristic classes of the tautological bundle can be expressed as iterated residues at infinity of some holomorphic functions of several variables. The results obtained for these cases can be expressed as special cases of one formula involving the Weyl group action on the characters of the natural representation of...

The S1-CW decomposition of the geometric realization of a cyclic set

Zbigniew Fiedorowicz, Wojciech Gajda (1994)

Fundamenta Mathematicae

We show that the geometric realization of a cyclic set has a natural, S 1 -equivariant, cellular decomposition. As an application, we give another proof of a well-known isomorphism between cyclic homology of a cyclic space and S 1 -equivariant Borel homology of its geometric realization.

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