Finiteness of Cannon--Thurston fibers
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912979193167872 |
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| author | Bhattacharyya, Indranil Halder, Rakesh Lazarovich, Nir Mj, Mahan |
| author_facet | Bhattacharyya, Indranil Halder, Rakesh Lazarovich, Nir Mj, Mahan |
| contents | Let $Y\to X$ be a proper map between proper hyperbolic metric spaces. A Cannon--Thurston map is a continuous extension $\partial Y \to \partial X$. We prove that in most known settings in which a Cannon--Thurston map exists it is uniformly finite-to-one. This answers a question due to Swarup from Bestvina's problem list and generalizes previous results of Cannon--Thurston, Kapovich--Lustig, Dowdall--Kapovich--Taylor and Ghosh. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_22428 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Finiteness of Cannon--Thurston fibers Bhattacharyya, Indranil Halder, Rakesh Lazarovich, Nir Mj, Mahan Geometric Topology Group Theory 20F65, 20F67 (Primary), 57M50 (Secondary) Let $Y\to X$ be a proper map between proper hyperbolic metric spaces. A Cannon--Thurston map is a continuous extension $\partial Y \to \partial X$. We prove that in most known settings in which a Cannon--Thurston map exists it is uniformly finite-to-one. This answers a question due to Swarup from Bestvina's problem list and generalizes previous results of Cannon--Thurston, Kapovich--Lustig, Dowdall--Kapovich--Taylor and Ghosh. |
| title | Finiteness of Cannon--Thurston fibers |
| topic | Geometric Topology Group Theory 20F65, 20F67 (Primary), 57M50 (Secondary) |
| url | https://arxiv.org/abs/2603.22428 |