Effective drilling and filling of tame hyperbolic 3-manifolds

Autor:	David Futer, Jessica Purcell, Saul Schleimer
Rok vydání:	2022
Předmět:	Mathematics - Geometric Topology 57K32 30F40 General Mathematics FOS: Mathematics Geometric Topology (math.GT) Mathematics::Differential Geometry Mathematics::Symplectic Geometry Mathematics::Geometric Topology
Zdroj:	Commentarii Mathematici Helvetici. 97:457-512
ISSN:	0010-2571
DOI:	10.4171/cmh/536
Popis:	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. Comment: 36 pages, 2 figures. In v3, theorems and definitions were renumbered to align with journal style. To appear in Commentarii Mathematici Helvetici
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c196e3977a4aed0a3034b5038122891b https://doi.org/10.4171/cmh/536 Zobrazit plný text záznamu