# Rigidity of pseudo-Anosov flows transverse to $\mathbb{R}$-covered foliations

### Sérgio R. Fenley

Florida State University, Tallahassee, USA

## Abstract

A foliation is $\mathbb{R}$-covered if the leaf space of the lifted foliation to the universal cover is homeomorphic to the set of real numbers. We show that, up to topological conjugacy, there are at most two pseudo-Anosov flows transverse to a fixed $\mathbb{R}$-covered foliation. If there are two transverse pseudo-Anosov flows, then the foliation is weakly conjugate to the stable foliation of an $\mathbb{R}$-covered Anosov flow. The proof uses the universal circle for $\mathbb{R}$-covered foliations.

## Cite this article

Sérgio R. Fenley, Rigidity of pseudo-Anosov flows transverse to $\mathbb{R}$-covered foliations. Comment. Math. Helv. 88 (2013), no. 3, pp. 643–676

DOI 10.4171/CMH/299