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arXiv · 2605.30956

Partial section III: for Anosov flows

Théo Marty
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Abstract

In the previous papers in the series, we characterized partial cross-sections for general flows, in the spirit of Fried's work on global cross-sections. In this paper, we deduce several consequences for Anosov flows. We provide a homology criterion for the existence of a partial cross-section in a given cohomology class. Additionally, there are at most finitely many partial cross-sections in that cohomology class. We deduce that on a 3-dimensional hyperbolic manifold, any Anosov flow is homologically full.

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Théo Marty. 2026-05-29. Partial section III: for Anosov flows. https://arxiv.org/abs/2605.30956

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