Pathways Workshop: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups: The veering ancestry graph and a conjecture of Ghys
Presenter
January 23, 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
A conjecture of Ghys asserts that any two transitive Anosov flows with orientable invariant foliations are almost orbit equivalent. In this talk, I will outline a connection between pseudo-Anosov flows and veering triangulations, and use it to reformulate Ghys’ conjecture in terms of properties of the veering ancestry graph. I will then discuss an algorithm whose implementation can be used to construct large subgraphs of this graph, and conclude by presenting the experimental data obtained.
This is joint work with Henry Segerman.