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geometrization conjecture

Contents

Contents

Idea

Every closed 3-manifold can be decomposed in a canonical way into pieces that each have one of eight types of geometric structure (…)

The proof of the geometrization conjecture implies that of

References

The conjecture was stated by William Thurston in 1982. The Ricci flow-strategy for the proof was devised by Richard Hamilton and the remaining technical problem of controlling the pinching was finally solved by Grigori Perelman.

  • Wikipedia, Geometrization conjecture

  • Laurent Bessieres, Gerard Besson, Michel Boileau, Sylvain Maillot, Joan Porti, Geometrisation of 3-manifolds (pdf)

Discussion for 3-dimensional orbifolds is in

  • Michel Boileau, Bernhard Leeb, Joan Porti, Geometrization of 3-Dimensional Orbifolds, Annals of Mathematics Second Series, Vol. 162, No. 1 (2005), pp. 195-290 (jstor:3597373)

  • Bruce Kleiner, John Lott, Geometrization of Three-Dimensional Orbifolds via Ricci Flow (arXiv:1101.3733)

Last revised on August 2, 2020 at 08:57:50. See the history of this page for a list of all contributions to it.