The Index of Dirac Operators on Incomplete Edge Spaces

[摘要] 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.

[关键词] Atiyah–Singer index theorem;Dirac operators;singular spaces;positive scalar curvature