$L^2$-Gamma index theorem for spacetimes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866913537574567936 |
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| author | Vertman, Orville Damaschke und Boris |
| author_facet | Vertman, Orville Damaschke und Boris |
| contents | We establish an $L^2$-Gamma index theorem for the Dirac operator on a globally hyperbolic manifold $M$ with Cauchy hypersurface $Σ$ being a Galois covering of a compact smooth manifold with Galois group $Γ$. Our argument rewrites the $L^2$-Gamma index in terms of the spectral flow, which is then connected to the usual geometric expressions. This extends the work of Bär and Strohmaier to some non-compact Cauchy hypersurfaces. The analysis here is based on intermediate results by the first author on $L^2$-Gamma Fredholm properties of the Dirac operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_05848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $L^2$-Gamma index theorem for spacetimes Vertman, Orville Damaschke und Boris Differential Geometry Spectral Theory 58J20, 58J45, secondary 35L03, 58J30, 58J40 We establish an $L^2$-Gamma index theorem for the Dirac operator on a globally hyperbolic manifold $M$ with Cauchy hypersurface $Σ$ being a Galois covering of a compact smooth manifold with Galois group $Γ$. Our argument rewrites the $L^2$-Gamma index in terms of the spectral flow, which is then connected to the usual geometric expressions. This extends the work of Bär and Strohmaier to some non-compact Cauchy hypersurfaces. The analysis here is based on intermediate results by the first author on $L^2$-Gamma Fredholm properties of the Dirac operator. |
| title | $L^2$-Gamma index theorem for spacetimes |
| topic | Differential Geometry Spectral Theory 58J20, 58J45, secondary 35L03, 58J30, 58J40 |
| url | https://arxiv.org/abs/2410.05848 |