A mod \(k\) index theorem (Q1187487)

First the authors introduce the notion of a \(\mathbb{Z}/k\)-manifold and a topological index \(t\)-ind for such a manifold. Then using \(b\)- pseudodifferential operators (totally characteristic pseudodifferential operators) they define also an analytic index \(a\)-ind. The main result in the paper is that for any compact \(\mathbb{Z}/k\)-manifold \(t\)-ind = \(a\)-ind holds. Finally the result is applied to Dirac operators.