Index of the Dirac operator on cone edge spaces

We derive a formula for the index of the Dirac operator on cone edge spaces, which are examples of stratified Riemannian spaces which look in a neighborhood of the singular locus like a bundle of cones over a smooth manifold. Such work goes back to Bismut and Cheeger in the 80's, with many other contributions, including the recent extension of the Hirzebruch signature formula on 4-dimensional Kaehler-Einstein manifolds with cone singularities along a surface by Atiyah and LeBrun.