JournalsjncgVol. 7, No. 3pp. 709–735

An equivariant noncommutative residue

  • Shantanu Dave

    University of Vienna, Austria
An equivariant noncommutative residue cover
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Abstract

Let Γ\Gamma be a finite group acting on a compact manifold MM and let A(M)\mathcal{A}(M) denote the algebra of classical complete symbols on MM. We determine all traces on the cross-product algebra A(M)Γ\mathcal{A}(M) \rtimes \Gamma as residues of certain meromorphic zeta functions. Further we compute the cyclic homology for A(M)Γ\mathcal{A}(M)\rtimes\Gamma in terms of the de Rham cohomology of the fixed point manifolds SMgS^*M^g. In the process certain new results on the homologies of general cross-product algebras are obtained.

Cite this article

Shantanu Dave, An equivariant noncommutative residue. J. Noncommut. Geom. 7 (2013), no. 3, pp. 709–735

DOI 10.4171/JNCG/132