The Index of Dirac Operators on Incomplete Edge Spaces
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چکیده
We derive a formula for the index of a Dirac operator on an 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.
منابع مشابه
The Index of Dirac Operators on Incomplete Edge Spaces
We derive a formula for the index of a Dirac operator on a compact, evendimensional 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.
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