Anosov vector fields and Fried sections
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866915471541927936 |
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| author | Bismut, Jean-Michel Shen, Shu |
| author_facet | Bismut, Jean-Michel Shen, Shu |
| contents | The purpose of this paper is to prove that if $Y$ is a compact manifold, if $Z$ is an Anosov vector field on $Y$, and if $F$ is a flat vector bundle, there is a corresponding canonical nonzero section $τ_ν\left(i_{Z}\right)$ of the determinant line $ν=\det H\left(Y,F\right)$. In families, this section is $C^{1}$ with respect to the canonical smooth structure on $ν$. When $F$ is flat on the total space of the corresponding fibration, our section is flat with respect to the Gauss-Manin connection on $ν$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_14583 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Anosov vector fields and Fried sections Bismut, Jean-Michel Shen, Shu Differential Geometry Dynamical Systems 11M36, 37D20, 37C30, 81Q20 The purpose of this paper is to prove that if $Y$ is a compact manifold, if $Z$ is an Anosov vector field on $Y$, and if $F$ is a flat vector bundle, there is a corresponding canonical nonzero section $τ_ν\left(i_{Z}\right)$ of the determinant line $ν=\det H\left(Y,F\right)$. In families, this section is $C^{1}$ with respect to the canonical smooth structure on $ν$. When $F$ is flat on the total space of the corresponding fibration, our section is flat with respect to the Gauss-Manin connection on $ν$. |
| title | Anosov vector fields and Fried sections |
| topic | Differential Geometry Dynamical Systems 11M36, 37D20, 37C30, 81Q20 |
| url | https://arxiv.org/abs/2405.14583 |