The index of dirac operators on incomplete edge spaces

Pierre Albin; Jesse Gell-Redman

doi:10.3842/SIGMA.2016.089

The index of dirac operators on incomplete edge spaces

Pierre Albin, Jesse Gell-Redman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English (US)
Article number	089
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	12
DOIs	https://doi.org/10.3842/SIGMA.2016.089
State	Published - Sep 8 2016

Keywords

Atiyah-Singer index theorem
Dirac operators
Positive scalar curvature
Singular spaces

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2016.089

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AB - 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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KW - Positive scalar curvature

KW - Singular spaces

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The index of dirac operators on incomplete edge spaces

Abstract

Keywords

ASJC Scopus subject areas

Online availability

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