Surjectivity of Cannon–Thurston maps in metric (graph) bundles
Year: 2026
Type: article
Abstract: Metric (graph) bundles generalize the notion of fiber bundles to the context of geometric group theory and were introduced by Mj and Sardar in 2012. Suppose X is a metric (graph) bundle over B such that the fibers are ( uniformly ) hyperbolic, and the total space X is also hyperbolic. In this generality, Mj–Sardar proved that the inclusion of a fiber into X admits a continuous extension to the (Gromov) boundary. In this article, we prove that such a continuous extension map between boundaries is surjective in the following two key settings: (1) the fibers are uniformly quasiisometric to a nonelementary hyperbolic group; (2) the fibers are one-ended hyperbolic metric spaces. Our result generalizes a theorem of Bowditch in which the fibers were assumed to be the hyperbolic plane, and it answers a question of Lazarovich–Margolis–Mj.
Source: Groups Geometry and Dynamics
DOI: 10.4171/ggd/1000
Author: Rakesh Halder
Institution: Tata Institute of Fundamental Research
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4416105382