The Index of Dirac Operators on Incomplete Edge Spaces

Symmetry Integrability and Geometry-Methods and Applications

article

Pierre Albin¹  Jesse Gell-Redman² 

[1] University of Illinois;Department of Mathematics, University of Melbourne

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

DOI  :  10.3842/SIGMA.2016.089

来源: National Academy of Science of Ukraine

【 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.

【 授权许可】

Unknown