The Fredholm index for operators of tensor product type

Abstract

We consider bisingular pseudodifferential operators which are pseudodifferential operators of tensor product type. These operators are defined on the product manifold $M_1\times M_2$, for closed manifolds $M_1$ and $M_2$. We prove a topological index theorem of product type. In addition, we show that the Fredholm index of elliptic bisingular operators equals the topological index, whenever the operator takes the form of an external tensor product of pseudodifferential operators, up to equivalence. To this end we construct a suitable double deformation groupoid and a Poincaré duality type homomorphism.

Revised version. To appear in JOT

References in corpus (2)

• An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
• Singular spaces, groupoids and metrics of positive scalar curvature