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arXiv · 2405.14583

Anosov vector fields and Fried sections

Jean-Michel Bismut·Shu Shen
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Abstract

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 $\tau_{\nu}\left(i_{Z}\right)$ of the determinant line $\nu=\det H\left(Y,F\right)$. In families, this section is $C^{1}$ with respect to the canonical smooth structure on $\nu$. When $F$ is flat on the total space of the corresponding fibration, our section is flat with respect to the Gauss-Manin connection on $\nu$.

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Jean-Michel Bismut, Shu Shen. 2024-05-23. Anosov vector fields and Fried sections. https://doi.org/10.1007/s00220-025-05400-8

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