An index of strongly Callias operators on Lorentzian manifolds with non-compact boundary

Maxim Braverman

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arXiv · 1807.03851

An index of strongly Callias operators on Lorentzian manifolds with non-compact boundary

Maxim Braverman

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Abstract

We consider a hyperbolic Dirac-type operator with growing potential on a a spatially non-compact globally hyperbolic manifold. We show that the Atiyah-Patodi-Singer boundary value problem for such operator is Fredholm and obtain a formula for this index in terms of the local integrals and the relative eta-invariant introduced by Braverman and Shi. This extends recent results of B\"ar and Strohmaier, who studied the index of a hyperbolic Dirac operator on a spatially compact globally hyperbolic manifold.

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Maxim Braverman. 2018-07-10. An index of strongly Callias operators on Lorentzian manifolds with non-compact boundary. https://arxiv.org/abs/1807.03851

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