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Effective drilling and filling of tame hyperbolic 3-manifolds
Purcell, Jessica Schleimer, Saul
Purcell, Jessica
Schleimer, Saul
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Journal article
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2022-08-12
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Mathematics
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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.
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David Futer, Jessica S. Purcell, Saul Schleimer, Effective drilling and filling of tame hyperbolic 3-manifolds. Comment. Math. Helv. 97 (2022), no. 3, pp. 457–512. DOI 10.4171/CMH/536
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EMS Press
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Commentarii Mathematici Helvetici: A Journal of the Swiss Mathematical Society (CMH), Vol. 97, No. 3
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