Adiabatic Limit and Analytic Torsion of Vector Bundles
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Acceso en línea: | |
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| _version_ | 1866914212958175232 |
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| author | Dai, Xianzhe Liu, Debin |
| author_facet | Dai, Xianzhe Liu, Debin |
| contents | For a vector bundle $E^{n+k}$ over a closed manifold $M^n$ with $k$ even and $n$ odd, we equip the metric with an adiabatic parameter, and prove that the index of $E$ is the same as the index of $M$. We also introduce an analog of analytic torsion on $E$ using the Witten Laplacian. Moreover, we prove that the Quillen metric associated with this analytic torsion coincides with that of $M$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_18602 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Adiabatic Limit and Analytic Torsion of Vector Bundles Dai, Xianzhe Liu, Debin Differential Geometry For a vector bundle $E^{n+k}$ over a closed manifold $M^n$ with $k$ even and $n$ odd, we equip the metric with an adiabatic parameter, and prove that the index of $E$ is the same as the index of $M$. We also introduce an analog of analytic torsion on $E$ using the Witten Laplacian. Moreover, we prove that the Quillen metric associated with this analytic torsion coincides with that of $M$. |
| title | Adiabatic Limit and Analytic Torsion of Vector Bundles |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2512.18602 |