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Title: An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
Authors: Baer, Christian
Strohmaier, Alexander
Issue Date: 2015
Publisher: Johns Hopkins University Press
Citation: BAER, C. and STROHMAIER, A., 2015. An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary. American Journal of Mathematics, In Press.
Abstract: We show that the Dirac operator on a compact globally hyperbolic Lorentzian spacetime with spacelike Cauchy boundary is a Fredholm operator if appropriate boundary conditions are imposed. We prove that the index of this operator is given by the same expression as in the index formula of Atiyah-Patodi-Singer for Riemannian manifolds with boundary. The index is also shown to equal that of a certain operator constructed from the evolution operator and a spectral projection on the boundary. In case the metric is of product type near the boundary a Feynman parametrix is constructed.
Description: © 2017. This is an author produced version of a paper accepted for publication in American Journal of Mathematics.
Version: Accepted for publication
URI: https://dspace.lboro.ac.uk/2134/20035
Publisher Link: http://muse.jhu.edu/journal/5
ISSN: 0002-9327
Appears in Collections:Published Articles (Maths)

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