Collapsing irreducible 3-manifolds with nontrivial fundamental group

DOI10.1007/s00222-009-0222-6zbMath1188.57013OpenAlexW2003036785WikidataQ56169984 ScholiaQ56169984MaRDI QIDQ2655176

Laurent Bessières, Michel Boileau, Sylvain Maillot, Gérard Besson, Joan Porti

Publication date: 22 January 2010

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00222-009-0222-6

zbMATH Keywords

geometrization conjecturePerelman's proofvolume-collapsing sequence

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) General geometric structures on low-dimensional manifolds (57M50)

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Cites Work

• A simple proof of Perelman's collapsing theorem for 3-manifolds
• Geometrization of 3-dimensional orbifolds
• A complete proof of the Poincaré and geometrization conjectures -- application of the Hamilton-Perelman theory of the Ricci flow
• Iteration on Teichmüller space
• Notes on Perelman's papers
• Volume and bounded cohomology
• Four-manifolds with positive curvature operator
• Hyperbolic structures on 3-manifolds. I: Deformation of acylindrical manifolds
• The Gromov invariant of links
• Finite propagation speed, kernel estimates for functions of the Laplace operator, and the geometry of complete Riemannian manifolds
• Lusternik-Schnirelmann category of 3-manifolds
• Three-manifolds with positive Ricci curvature
• On the structure of complete manifolds of nonnegative curvature
• Volume collapsed three-manifolds with a lower curvature bound
• MULTICOMPLEXES, BOUNDED COHOMOLOGY AND ADDITIVITY OF SIMPLICIAL VOLUME
• A Compactness Property for Solutions of the Ricci Flow
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