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Effective bilipschitz bounds on drilling and filling
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Futer, David, Purcell, Jessica S. and Schleimer, Saul (2022) Effective bilipschitz bounds on drilling and filling. Geometry & Topology, 26 (3). pp. 1077-1188. doi:10.2140/gt.2022.26.1077 ISSN 1364-0380.
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WRAP-Effective-bilipschitz-bounds-drilling-filling-22.pdf - Accepted Version - Requires a PDF viewer. Download (1360Kb) | Preview |
Official URL: http://dx.doi.org/10.2140/gt.2022.26.1077
Abstract
We prove explicit bilipschitz bounds on the change in metric between the thick part of a cusped hyperbolic 3–manifold Nand the thick part of any of its long Dehn fillings. Given a bilipschitz constant J>1 and a thickness constant ϵ>0, we quantify how long a Dehn filling suffices to guarantee a J–bilipschitz map on ϵ–thick parts. A similar theorem without quantitative control was previously proved by Brock and Bromberg, applying Hodgson and Kerckhoff’s theory of cone deformations. We achieve quantitative control by bounding the analytic quantities that control the infinitesimal change in metric during the cone deformation.
| Item Type: | Journal Article | ||||||
|---|---|---|---|---|---|---|---|
| Subjects: | Q Science > QA Mathematics | ||||||
| Divisions: | Faculty of Science, Engineering and Medicine > Science > Mathematics | ||||||
| Library of Congress Subject Headings (LCSH): | Three-manifolds (Topology), Geometry, Hyperbolic, Dehn surgery (Topology), Kleinian groups , Riemann surfaces , Knot theory | ||||||
| Journal or Publication Title: | Geometry & Topology | ||||||
| Publisher: | Geometry & Topology Publications | ||||||
| ISSN: | 1364-0380 | ||||||
| Official Date: | 3 August 2022 | ||||||
| Dates: |
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| Volume: | 26 | ||||||
| Number: | 3 | ||||||
| Page Range: | pp. 1077-1188 | ||||||
| DOI: | 10.2140/gt.2022.26.1077 | ||||||
| Status: | Peer Reviewed | ||||||
| Publication Status: | Published | ||||||
| Access rights to Published version: | Open Access (Creative Commons) | ||||||
| Date of first compliant deposit: | 12 October 2022 | ||||||
| Date of first compliant Open Access: | 12 October 2022 |
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