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Geometrization conjecture
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Details
Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed into submanifolds that have geometric structures. The geometrization conjecture is an analogue for 3-manifolds of the uniformization theorem for surfaces. It was proposed by William Thurston in 1982, and implies several other conjectures, such as the Poincaré conjecture and Thurston's elliptization conjecture. Thurston's geometrization theorem, or hyperbolization theorem, states that Haken manifolds satisfy the conclusion of geometrization conjecture. Thurston announced a proof in the 1980s and since then several complete proofs have appeared in print. Grigori Perelman sketched a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery. There are now four different manuscripts with details of the proof. The Poincaré conjecture and the spherical space form conjecture are corollaries of the geometrization conjecture, although there are shorter proofs of the former that do not lead to the geometrization conjecture.
Weitere Informationen
- Allgemeine Informationen
- GTIN 09786130272982
- Editor Frederic P. Miller, Agnes F. Vandome, John McBrewster
- Sprache Englisch
- Größe H220mm x B150mm x T5mm
- Jahr 2010
- EAN 9786130272982
- Format Fachbuch
- ISBN 978-613-0-27298-2
- Titel Geometrization conjecture
- Autor Frederic P. Miller
- Untertitel 3-manifold, Submanifold, Uniformization theorem, Surface, William Thurston, Poincaré conjecture, Thurston elliptization conjecture, Haken manifold, Grigori Perelman, Ricci flow
- Gewicht 130g
- Herausgeber Alphascript Publishing
- Anzahl Seiten 76
- Genre Mathematik
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