2024/11/23 by Danny Calegari, Calegari, Danny, Ino Loukidou +1
Agricultural and Biological Sciences · Mathematics · #Garlic and Onion Studies #Plant Physiology and Cultivation Studies #math.DS #math.GR #math.GT
paper · pdf · doi:10.48550/arxiv.2411.15610
openalex publication_date 2024/11/23 · openalex created_date 2024/12/04 · openalex updated_date 2026/07/28
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 π1(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 left orders.