Abstract:
We derive a formula for the index of a Dirac operator on a compact, even-dimensional incomplete edge space satisfying a “geometric Witt condition”. We accomplish this by cutting off to a smooth manifold with boundary, applying the Atiyah–Patodi–Singer index theorem, and taking a limit. We deduce corollaries related to the existence of positive scalar curvature metrics on incomplete edge spaces.
Keywords:Atiyah–Singer index theorem; Dirac operators; singular spaces; positive scalar curvature.