Relatively hyperbolic metric bundles and Cannon-Thurston map
| Autor: | Krishna, Swathi |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 40 pages, 4 figures |
| Databáze: | arXiv |
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