Journal of Noncommutative Geometry

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Volume 7, Issue 3, 2013, pp. 709–735
DOI: 10.4171/JNCG/132

Published online: 2013-09-24

An equivariant noncommutative residue

Shantanu Dave[1]

(1) University of Vienna, Austria

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

Keywords: Noncommutative residue, cyclic homology, cross-product algebra

Dave Shantanu: An equivariant noncommutative residue. J. Noncommut. Geom. 7 (2013), 709-735. doi: 10.4171/JNCG/132