Zippers

If M is a hyperbolic 3-manifold fibering over the circle, the fundamental group of M acts faithfully by homeomorphisms on a circle (the circle at infinity of the universal cover of the fiber), preserving a pair of invariant (stable and unstable) laminations.Many different kinds of dynamical structures (e.g., taut foliations, quasigeodesic or pseudo-Anosov flows) are known to give rise to universal circles -a circle with a faithful 1 .M /-action preserving a pair of invariant laminations -and these universal circles play a key role in relating the dynamical structure to the geometry of M .In this paper we introduce the idea of zippers, which give a new and direct way to construct universal circles, streamlining the known constructions in many cases, and giving a host of new constructions in others.In particular, zippers (and their associated universal circles) may be constructed directly from uniform quasimorphisms or from uniform actions.