Pseudo-Anosov flows and the geometry of Anosov-like group actions
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914561457651712 |
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| author | Barthelmé, Thomas Mann, Kathryn Paulet, Neige Zalloum, Abdul |
| author_facet | Barthelmé, Thomas Mann, Kathryn Paulet, Neige Zalloum, Abdul |
| contents | We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed $3$-manifold (and more general Anosov-like actions) can be seen as an isometric action on a Gromov-hyperbolic space. When the flow is not $\R$-covered, we show that this action admits elements that are weakly properly discontinuous and deduce that elements of $π_1(M)$ that do \emph{not} represent a periodic orbit of the flow are generic for any word metric coming from a finite generating set. We also give a number of other geometric group-theoretic results for Anosov-like group actions on bifoliated planes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_12837 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Pseudo-Anosov flows and the geometry of Anosov-like group actions Barthelmé, Thomas Mann, Kathryn Paulet, Neige Zalloum, Abdul Dynamical Systems Geometric Topology We show that the action on its orbit space induced by a pseudo-Anosov flow on a closed $3$-manifold (and more general Anosov-like actions) can be seen as an isometric action on a Gromov-hyperbolic space. When the flow is not $\R$-covered, we show that this action admits elements that are weakly properly discontinuous and deduce that elements of $π_1(M)$ that do \emph{not} represent a periodic orbit of the flow are generic for any word metric coming from a finite generating set. We also give a number of other geometric group-theoretic results for Anosov-like group actions on bifoliated planes. |
| title | Pseudo-Anosov flows and the geometry of Anosov-like group actions |
| topic | Dynamical Systems Geometric Topology |
| url | https://arxiv.org/abs/2605.12837 |