Loughborough University
Leicestershire, UK
LE11 3TU
+44 (0)1509 263171
Loughborough University

Loughborough University Institutional Repository

Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/20035

Title: An index theorem for Lorentzian manifolds with compact spacelike Cauchy boundary
Authors: Baer, Christian
Strohmaier, Alexander
Issue Date: 2018
Publisher: Johns Hopkins University Press
Citation: BAER, C. and STROHMAIER, A., 2018. 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)

Files associated with this item:

File Description SizeFormat
BAR_lorentz-index.pdfAccepted version2.28 MBAdobe PDFView/Open


SFX Query

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.