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arXiv · 2204.01073

Relatively hyperbolic metric bundles and Cannon-Thurston map

Swathi Krishna
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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 $i: A\to B$, we show that the pullback $Y$ is strongly relatively hyperbolic and the map $Y\to X$ 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.

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Swathi Krishna. 2022-04-03. Relatively hyperbolic metric bundles and Cannon-Thurston map. https://arxiv.org/abs/2204.01073

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