Collapsing irreducible 3-manifolds with nontrivial fundamental group

• 成果类型: Article
• 署名作者: Bessieres, L.; Besson, G.; Boileau, M.; Maillot, S.; Porti, J.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Communaute Universite Grenoble Alpes; Universite Grenoble Alpes (UGA); Universite Federale Toulouse Midi-Pyrenees (ComUE); Universite de Toulouse; Institut National des Sciences Appliquees de Toulouse; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite de Montpellier; Autonomous University of Barcelona
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-009-0222-6
• 发表日期: 2010
• 页码: 435-460
• 关键词: riemannian-manifolds; ricci flow; CURVATURE; geometrization; operator

摘要

Let M be a closed, orientable, irreducible, non-simply connected 3-manifold. We prove that if M admits a sequence of Riemannian metrics which volume-collapses and whose sectional curvature is locally controlled, then M is a graph manifold. This is the last step in Perelman's proof of Thurston's Geometrisation Conjecture.