Geometry & Topology Seminar: Zippers!

Abstract: 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 (eg taut foliations, quasigeodesic or pseudo-Anosov flows) are known to give rise to universal circles - i.e. a circle with a faithful pi_1(M) action preserving a pair of invariant laminations - and these play a key role in relating the dynamical structure to the geometry of M. In this talk we introduce the idea of *Zippers*, which give a new and direct way to construct universal circles, streamlining the known construction in some cases, and giving a host of new constructions in others. This is joint work with Danny Calegari.