Year: 2025
Type: article
Abstract: PRANAB SARDAR Metric (graph) bundles were defined by Mj and Sardar (Geom. Funct. Anal. 22 (2012) 1636-1707).In this paper, we introduce the notion of morphisms and pullbacks of metric (graph) bundles.Given a metric (graph) bundle X over B where X and all the fibers are uniformly (Gromov) hyperbolic and nonelementary, and a Lipschitz quasiisometric embedding i W A ! B, we show that the pullback i X is hyperbolic and the map i W i X !X admits a continuous boundary extension, ie the Cannon-Thurston (CT) map @i W @.i X / !@X .As an application of our theorem, we show that given a short exact sequence of nonelementary hyperbolic groups 1 !N !G ! Q ! 1 and a finitely generated quasiisometrically embedded subgroupWe then derive several interesting properties of the CT map.20F65 1. Introduction 2667 2. Hyperbolic metric spaces 2670 3. Metric bundles 2695 4. Geometry of metric bundles 2713 5. Cannon-Thurston maps for pullback bundles 2721 6. Applications, examples and related results 2737Appendix.Flaring in a metric bundle and its canonical metric graph bundle 2751
Source: Algebraic & Geometric Topology
Authors: Swathi Krishna, Pranab Sardar
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W3044863099