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Effective drilling and filling of tame hyperbolic 3-manifolds
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Futer, David, Purcell, Jessica and Schleimer, Saul (2022) Effective drilling and filling of tame hyperbolic 3-manifolds. Commentarii Mathematici Helvetici, 97 (3). pp. 457-512. doi:10.4171/CMH/536 ISSN 0010-2571.
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WRAP-Effective-drilling-and-filling-of-tame-hyperbolic-3-manifolds-Schleimer-2022.pdf - Published Version - Requires a PDF viewer. Available under License Creative Commons Attribution 4.0. Download (508Kb) | Preview |
Official URL: http://dx.doi.org/10.4171/CMH/536
Abstract
We give effective bilipschitz bounds on the change in metric between thick parts of a cusped hyperbolic 3-manifold and its long Dehn fillings. In the thin parts of the manifold, we give effective bounds on the change in complex length of a short closed geodesic. These results quantify the filling theorem of Brock and Bromberg, and extend previous results of the authors from finite volume hyperbolic 3-manifolds to any tame hyperbolic 3-manifold. To prove the main results, we assemble tools from Kleinian group theory into a template for transferring theorems about finite-volume manifolds into theorems about infinite-volume manifolds. We also prove and apply an infinite-volume version of the 6-Theorem.
| Item Type: | Journal Article | |||||||||
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| Subjects: | Q Science > QA Mathematics | |||||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | |||||||||
| Library of Congress Subject Headings (LCSH): | Dehn surgery (Topology), Hyperbolic spaces, Kleinian groups, Three-manifolds (Topology) | |||||||||
| Journal or Publication Title: | Commentarii Mathematici Helvetici | |||||||||
| Publisher: | European Mathematical Society Publishing House | |||||||||
| ISSN: | 0010-2571 | |||||||||
| Official Date: | 12 August 2022 | |||||||||
| Dates: |
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| Volume: | 97 | |||||||||
| Number: | 3 | |||||||||
| Page Range: | pp. 457-512 | |||||||||
| DOI: | 10.4171/CMH/536 | |||||||||
| Status: | Peer Reviewed | |||||||||
| Publication Status: | Published | |||||||||
| Access rights to Published version: | Open Access (Creative Commons) | |||||||||
| Date of first compliant deposit: | 11 October 2022 | |||||||||
| Date of first compliant Open Access: | 12 October 2022 | |||||||||
| RIOXX Funder/Project Grant: |
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