Pathways Workshop: Topological and Geometric Structures in Low Dimensions & Geometry and Dynamics for Discrete Subgroups of Higher Rank Lie Groups: Taut foliations, transverse flows, and Floer homology
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
The L-space conjecture makes a prediction about which rational homology spheres can admit a taut foliation. But where could the predicted taut foliations "come from"? Must they be compatible with “natural” geometric structures on the 3-manifold? In this talk, I'll discuss forthcoming work with John Baldwin and Matt Hedden, where we address a type of geography problem for taut foliations. In particular, we show that when K is a fibered strongly quasipositive knot, large surgeries along K can never admit a taut foliation which is ‘’compatible’’ with the natural flow on the Dehn surgered manifold. I'll explain why this is surprising, and if time permits, sketch the proof. No background will be assumed — all are welcome!