Relative index theorem in \(K\)-homology (Q280803)

The Gromov-Lawson Theorem says that the relative index for the Dirac operators on complete non-compact Riemannian manifolds is independent of the underlying structure on the set where they coincide. The author of the paper under review generalizes the relative index theorem of Gromov and Lawson to the context of \(K\)-homology of a \(C^*\)-algebra \(A\) related to the Dirac operator on sections of a bundle of projective Hilbert \(A\)-modules over a complete non-compact Riemannian manifold. A helpful example at the end of the paper is considered.