\(K\)-homology and regular singular Dirac-Schrödinger operators on even-dimensional manifolds (Q1382050)

The authors study index problems associated to Dirac type operators on incomplete Riemann manifolds with asymptotically cone-like singularities. The behavior of the Dirac operator near these singularities is restricted by the regular-singular assumption. The authors show that these operators define classes in the \(K\)-homology of the metric completion of such manifolds. These are described as Kasparov products of a \(K\)-homology class on the incomplete manifold and a certain \(K\)-cohomology class determined by the zeroth order part of the operator. Among the tools used in this paper are the analysis of regular-singular operators and techniques for studying analytic \(K\)-homology cycles on singular spaces and their open dense subsets.