Paper
Universal circles for Anosov foliations
Authors
Ellis Buckminster, Samuel J. Taylor
Abstract
Thurston introduced the notion of a universal circle associated to a taut foliation of a -manifold as a way of organizing the ideal circle boundaries of its leaves into a single circle action. Calegari--Dunfield proved that every taut foliation of an atoroidal -manifold has a universal circle, but the uniqueness (or lack-thereof) of this structure remains rather mysterious.
In this paper, we consider the foliations associated to an Anosov flow on , showing that several constructions of a universal circle in the literature are typically distinct. Moreover, the underlying action of the Calegari--Dunfield leftmost universal circle is generally not even conjugate to the universal circle arising from the boundary of the flow space of . Our primary tool is a way to use the flow space of to parameterize the circle bundle at infinity of 's invariant foliations.