Journal article
The index of dirac operators on incomplete edge spaces
P Albin, J Gell-Redman
Symmetry Integrability and Geometry Methods and Applications Sigma | NATL ACAD SCI UKRAINE, INST MATH | Published : 2016
Open access
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.
Grants
Awarded by National Science Foundation
Funding Acknowledgements
P.A. was supported by NSF grant DMS-1104533 and Simons Foundation grant #317883. The authors are happy to thank Rafe Mazzeo and Richard Melrose for many useful and interesting discussions. They are also grateful to the comments of the anonymous referees, particularly their suggestion of Remark 3.5.