Videos

Pathways Workshop: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups: Psuedo-Anosov flows and orbit spaces

Presenter
January 21, 2026
Keywords:
  • low-dimensional topology
  • geometric structures
  • homogeneous dynamics
  • Anosov representations
  • Higher rank Lie groups
  • symmetric spaces of non- compact type
MSC:
  • 57M50 - General geometric structures on low-dimensional manifolds
  • 57M60 - Group actions on manifolds and cell complexes in low dimensions
  • 57N16 - Geometric structures on manifolds of high or arbitrary dimension
  • 57S25 - Groups acting on specific manifolds
  • 22E40 - Discrete subgroups of Lie groups
  • 22F30 - Homogeneous spaces
  • 37E05 - Dynamical systems involving maps of the interval
  • 37E10 - Dynamical systems involving maps of the circle
  • 37E30 - Dynamical systems involving homeomorphisms and diffeomorphisms of planes and surfaces
  • 37E35 - Flows on surfaces
  • 30F60 - Teichmüller theory for Riemann surfaces
  • 32G15 - Moduli of Riemann surfaces
  • Teichmüller theory (complex-analytic aspects in several variables)]
  • 30F40 - Kleinian groups (aspects of compact Riemann surfaces and uniformization)
Abstract
I will introduce the audience to pseudo-Anosov flows and related structures on 3-manifolds, and present a simple proof of a theorem of Barbot that says such flows can be completely reconstructed from a group acting on the plane. This is the setting for much of my recent joint work (with Barthelmé, Bonatti, Fenley and others); time permitting I will give some idea of this theory.