Thurston’s Theory of 3-Manifolds

DOI10.1007/978-3-030-55928-1_4zbMath1479.57059OpenAlexW3111722577MaRDI QIDQ3384095

Sadayoshi Kojima

Publication date: 14 December 2021

Published in: In the Tradition of Thurston (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-3-030-55928-1_4

zbMATH Keywords

3-manifoldshyperbolic geometryvirtual Haken conjecturegeometrization conjecturevirtual fiber conjecture

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) Biographies, obituaries, personalia, bibliographies (01A70) General geometric structures on low-dimensional manifolds (57M50) Group actions on manifolds and cell complexes in low dimensions (57M60) Research exposition (monographs, survey articles) pertaining to manifolds and cell complexes (57-02) Hyperbolic 3-manifolds (57K32) General topology of 3-manifolds (57K30)

Cites Work

• The virtual Haken conjecture (with an appendix by Ian Agol, Daniel Groves and Jason Manning).
• Immersing almost geodesic surfaces in a closed hyperbolic three manifold
• Thurston's vision and the virtual fibering theorem for 3-manifolds
• Geometrization of 3-dimensional orbifolds
• Hyperbolic structures on 3-manifolds. I: Deformation of acylindrical manifolds
• Homotopy equivalences of 3-manifolds with boundaries
• Convergence groups and Seifert fibered 3-manifolds
• Codimension-1 subgroups and splittings of groups
• Three-dimensional orbifolds and cone-manifolds
• Non-singular solutions of the Ricci flow on three-manifolds
• Three-manifolds with positive Ricci curvature
• Special cube complexes
• On irreducible 3-manifolds which are sufficiently large
• Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms
• Strong rigidity of Q-rank 1 lattices
• Geometric group theory and 3-manifolds hand in hand: the fulfillment of Thurston’s vision
• A boundary criterion for cubulation
• The evolution of geometric structures on 3-manifolds
• Criteria for virtual fibering
• On the geometry and dynamics of diffeomorphisms of surfaces
• A Unique Decomposition Theorem for 3-Manifolds
• Three dimensional manifolds, Kleinian groups and hyperbolic geometry
• Renormalization and 3-Manifolds Which Fiber over the Circle
• The Geometries of 3-Manifolds
• Hyperbolic manifolds and discrete groups
• Four-manifolds with positive isotropic curvature
• Convergence groups are Fuchsian groups
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