Completion of the Proof of the Geometrization Conjecture

Abstract

This article is a sequel to the book `Ricci Flow and the Poincare Conjecture' by the same authors. Using the main results of that book we establish the Geometrization Conjecture for all compact, orientable three-manifolds following the approach indicated by Perelman in his preprints on the subject. This approach is to study the collapsed part of the manifold as time goes to infinity in a Ricci flow with surgery. The main technique for this study is the theory of Alexandrov spaces. This theory gives local models for the collapsed part of the manifold. These local models can be glued together to prove that the collapsed part of the manifold is a graph manifold with incompressible boundary. From this and previous results, geometrization follows easily.

84 pages

References in corpus (5)

• Ricci flow with surgery on three-manifolds
• Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• Ricci Flow and the Poincare Conjecture
• Perelman's Stability Theorem
• Weak collapsing and geometrisation of aspherical 3-manifolds

Cited by in corpus (11)

• Ricci Solitons and Einstein-Scalar Field Theory
• Survey on aspherical manifolds
• Metric flips with Calabi ansatz
• Perelman's Ricci Flow in Topological Quantum Gravity
• Thurston's Spinning Construction and Solutions to the Hyperbolic Gluing Equations for Closed Hyperbolic 3-Manifolds
• On the topology of locally volume collapsed Riemannian 3-orbifolds
• Equivariant Ricci flow with surgery and applications to finite group actions on geometric 3-manifolds
• Collapsing three-dimensional closed Alexandrov spaces with a lower curvature bound
• Minimal volume and simplicial norm of visibility n-manifolds and compact 3-manifolds
• G-monopole invariants on some connected sums of 4-manifolds
• Remarks on the Birch-Swinnerton-Dyer conjecture