K-homology classes of elliptic uniform pseudodifferential operators

TL;DR

This paper demonstrates that elliptic uniform pseudodifferential operators on manifolds of bounded geometry define classes in uniform K-homology, depending solely on their principal symbols, linking operator theory with topological invariants.

Contribution

It establishes a new connection between elliptic uniform pseudodifferential operators and uniform K-homology, emphasizing the role of principal symbols in this relationship.

Findings

Elliptic uniform pseudodifferential operators define classes in uniform K-homology.

These classes depend only on the principal symbol of the operators.

The work extends the understanding of index theory on manifolds of bounded geometry.

Abstract

We show that an elliptic uniform pseudodifferential operator over a manifold of bounded geometry defines a class in uniform K-homology, and that this class only depends on the principal symbol of the operator.