The Index of Dirac Operators on Incomplete Edge Spaces

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.

References in corpus (2)

• Analysis on singular spaces: Lie manifolds and operator algebras
• Boundary value problems for elliptic wedge operators: the first order case

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