Year: 2026
Type: preprint
Abstract: Suppose that $M$ is a finite-volume cusped hyperbolic three-manifold, equipped with a veering triangulation $\mathcal{V}$. We prove that the action of the fundamental group of $M$ on the veering two-sphere is a geometrically finite convergence action. Applying a result of Yaman, we deduce that the veering two-sphere is equivariantly homeomorphic to the boundary of hyperbolic space. As an application, we obtain Cannon-Thurston maps associated to veering triangulations. If $\mathcal{V}$ is layered we recover the classical Cannon-Thurston map. If it is not we obtain Cannon-Thurston maps that do not come from surface subgroups. These are the first such examples in the cusped case. Finally, we implement an algorithm to draw approximations of these Cannon-Thurston maps. This improves upon previous approximations obtained by Thurston and others.
Source: arXiv (Cornell University)
Institution: Cornell University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Veering Triangulations and Visualization, Three- and Four-Dimensional Triangulations and Mathematical Visualization, Mathematical Sciences Research Institute (MSRI), G2879864793, Institute for Computational and Experimental Research in Mathematics, G329468232, G3375465512, G4299339130, G4663222005, G4972001970, G5058101487, G6019427330, G6363417690, G6389258043, G6453481984, G6505494016, G6758477442, G7048127755, G7342182005
OpenAlex ID: W7213367997