Equivariant homology for pseudo-differential operators

Abstract

We compute the cyclic homology for the cross-product al- gebra $A(M)⋊\Gamma$ of the algebra of complete symbols on a compact man- ifold $M$ with action of a finite group $\Gamma$. A spectral sequence argument shows that these groups can be identified using deRham cohomology of the fixed point manifolds $S^{\ast }{M}^g$ . In the process we obtain new re- sults about the homologies of general cross-product algebras and provide explicit identification of the homologies for $C^{\infty }(M)⋊\Gamma$.

25pages

References in corpus (1)

• Homology of pseudodifferential operators I. Manifolds with boundary