Relatively hyperbolic metric bundles and Cannon-Thurston map

2022/01/01 by Swathi Krishna, Krishna, Swathi
Mathematics · #20F65 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2204.01073

Abstract

Given a metric (graph) bundle X over B where all the fibres are strongly relatively hyperbolic and nonelementary we show that, under certain conditions, X is strongly hyperbolic relative to a collection of maximal cone-subbundles of horosphere-like spaces. Further, given a coarsely Lipschitz qi embedding i: A→ B, we show that the pullback Y is strongly relatively hyperbolic and the map Y→ X admits a Cannon-Thurston (CT) map. As an application, we prove a group-theoretic analogue of this result for a relatively hyperbolic extension of groups.

Citations

• Propagating quasiconvexity from fibers
• Relative hyperbolicity, trees of spaces and Cannon-Thurston maps
• Dehn filling in relatively hyperbolic groups
• On a theorem of Scott and Swarup

Related

• Surjectivity of the Cannon--Thurston map in metric (graph) bundles
• Strong Property (T) and relatively hyperbolic groups
• Cubulating Drilled bundles over graphs
• From Hierarchical to Relative Hyperbolicity
• On Cannon-Thurston maps for relatively hyperbolic groups