arXiv:1312.4241 Abstract | arXiv Analytics

arXiv:1312.4241 [math.DG]Abstract References Reviews Resources

The index of Dirac operators on incomplete edge spaces

Published 2013-12-16, updated 2014-11-29Version 2

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.

Comments: Significantly revised and edited. Non-zero local boundary term identified and computed in special cases. 41 pages, 4 figures

Categories: math.DG, math.AP

Keywords: dirac operator, geometric witt condition, atiyah-patodi-singer index theorem, positive scalar curvature metrics, deduce corollaries

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