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Journal of Operator Theory

Volume 90, Issue 2, Autumn 2023  pp. 425-451.

The Fredholm index for operators of tensor product type

Authors:  Karsten Bohlen
Author institution: Universitaet Regensburg, Regensburg, 93040, Germany

Summary:  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 Poincare duality type homomorphism.

Keywords: pseudodifferential, bisingular, index theory

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