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arXiv · 2605.12837

Pseudo-Anosov flows and the geometry of Anosov-like group actions

Thomas Barthelmé·Kathryn Mann·Neige Paulet·Abdul Zalloum
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Abstract

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 $\pi_1(M)$ 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.

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Thomas Barthelmé, Kathryn Mann, Neige Paulet, Abdul Zalloum. 2026-05-13. Pseudo-Anosov flows and the geometry of Anosov-like group actions. https://arxiv.org/abs/2605.12837

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