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arXiv · 1702.01178

A note on self orbit equivalences of Anosov flows and bundles with fiberwise Anosov flows

Thomas Barthelmé·Andrey Gogolev
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Abstract

We show that a self orbit equivalence of a transitive Anosov flow on a $3$-manifold which is homotopic to identity has to either preserve every orbit or the Anosov flow is $\mathbb{R}$-covered and the orbit equivalence has to be of a specific type. This result shows that one can remove a relatively unnatural assumption in a result of Farrell and Gogolev about the topological rigidity of bundles supporting a fiberwise Anosov flow when the fiber is $3$-dimensional.

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Thomas Barthelmé, Andrey Gogolev. 2017-02-03. A note on self orbit equivalences of Anosov flows and bundles with fiberwise Anosov flows. https://arxiv.org/abs/1702.01178

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