L²-Gamma-Fredholmness for spacetimes

2024/10/01 by Orville Damaschke, Damaschke, Orville
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Cosmology and Gravitation Theories #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Operator Algebras (math.OA)

paper · pdf · doi:10.48550/arxiv.2410.00879

openalex publication_date 2024/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let M be a temporal compact globally hyperbolic manifold with Cauchy hypersurface Σ which is a Galois covering with respect to a discrete group Γ of automorphisms such that the quotient Σ/Γ is compact without boundary. We will show Fredholmness of a (spatial) Γ-invariant Lorentzian Dirac operator under (anti) Atiyah-Patodi-Singer boundary conditions in the von Neumann sense, known as (L²-)Γ-Fredholmness. The results already have been published for a simpler setting in arXiv:2107.08532. This version is only focused on the Fredholmness part, based on previous results from arXiv:2409.17344, and also generalised (anti) Atiyah-Patodi-Singer boundary conditions are going to be considered as well.

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