$L^2$-Gamma-Fredholmness for spacetimes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913525672181760 |
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| author | Damaschke, Orville |
| author_facet | Damaschke, Orville |
| contents | 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 ($L^2$-)$Γ$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_00879 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^2$-Gamma-Fredholmness for spacetimes Damaschke, Orville Differential Geometry Operator Algebras 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 ($L^2$-)$Γ$-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. |
| title | $L^2$-Gamma-Fredholmness for spacetimes |
| topic | Differential Geometry Operator Algebras |
| url | https://arxiv.org/abs/2410.00879 |