Universal bounds for hyperbolic Dehn surgery

• 成果类型: Article
• 署名作者: Hodgson, CD; Kerckhoff, SP
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.162.367
• 发表日期: 2005
• 页码: 367-421
• 关键词: convergence theorem; volume; 3-manifolds; MANIFOLDS; RIGIDITY; tubes

摘要

This paper gives a quantitative version of Thurston's hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of nonhyperbolic Dehn fillings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn filling. The proofs involve the construction of a family of hyperbolic cone-manifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.