Stable loops and almost transverse surfaces
Michael P. Landry
Washington University in St. Louis, USA
Abstract
We use veering triangulations to study homology classes on the boundary of the cone over a fibered face of a compact fibered hyperbolic three-manifold. This allows us to give a handson proof of an extension of Mosher’s transverse surface theorem to the setting of manifolds with boundary. We also show that the cone over a fibered face is dual to the cone generated by the homology classes of a canonical finite collection of curves called minimal stable loops living in the associated veering triangulation.
Cite this article
Michael P. Landry, Stable loops and almost transverse surfaces. Groups Geom. Dyn. 17 (2023), no. 1, pp. 35–75
DOI 10.4171/GGD/655