Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 12 (2016), 089, 45 pages      arXiv:1312.4241

The Index of Dirac Operators on Incomplete Edge Spaces

Pierre Albin a and Jesse Gell-Redman b
a) University of Illinois, Urbana-Champaign, USA
b) Department of Mathematics, University of Melbourne, Melbourne, Australia

Received November 02, 2015, in final form August 30, 2016; Published online September 08, 2016

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.

Key words: Atiyah-Singer index theorem; Dirac operators; singular spaces; positive scalar curvature.

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