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The geometrisation conjecture was proposed by William Thurston in the mid s in order to classify compact 3-manifolds by means of a.
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Daskalopoulos and C. Kenig , Degenerate diffusions. Initial value problems and local regularity theory , II , Journal of Differential Geometry , vol.

Gallot, D. Hulin, and J. Lafontaine , Riemannian geometry. Universitext , Gururaja, H. Maity, and.

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Seshadri , On Wilking's criterion for the Ricci flow. Gro91 and. Gromov , Sign and geometric meaning of curvature , Rend. Milano , vol. Katz, P. Pansu and S.


  1. Ricci Flow and Geometric Applications!
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Giesen and P. Topping , Ricci flows with unbounded curvature. Greene and H. Gao and Y. Hamilton , Four-manifolds with positive curvature operator , Journal of Differential Geometry , vol. Richard and. Hamilton , The formation of singularities in the Ricci flow , Surveys in differential geometry , pp. Jost , Riemannian geometry and geometric analysis , Kapovitch , Perelman???

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Kleiner and J. Lott , Notes on Perelman??? Klingenberg ,?? Gary and. Lieberman , Second order parabolic differential equations , Singapore : World Scientific. Mario, J. Micallef, and. Moore , Minimal two-spheres and the topology of manifolds with positive curvature on totally isotropic two-planes. Morgan and G. Huy and. Nguyen , Isotropic curvature and the Ricci flow , Int. IMRN , issue. Nw07a, J. Ni, and. Ni and B. Wu , Complete manifolds with nonnegative curvature operator , Proceedings of the American Mathematical Society , vol.

Per97 and. Perelman , Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers , Comparison geometry , pp. Per02 and. Perelman , The entropy formula for the Ricci flow and its geometric applications. ArXiv Mathematics e-prints , Per03 and. Skip to content. Abstract In this paper we prove that the moduli space of metrics with positive scalar curvature of an orientable compact three-manifold is path-connected.

Bartnik and J. Besson, M. Boileau, S. Maillot, and J. Porti, "Collapsing irreducible 3-manifolds with nontrivial fundamental group," Invent. Besson, S. Maillot, M. Boileau, and J. Botvinnik and P. Gilkey, "Metrics of positive scalar curvature on spherical space forms," Canad.

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Cao and X. Carr, "Construction of manifolds of positive scalar curvature," Trans. Chen, P. Lu, and G. Tian, "A note on uniformization of Riemann surfaces by Ricci flow," Proc. Differential Geom. Colding and W. Minicozzi II, "Estimates for the extinction time for the Ricci flow on certain 3-manifolds and a question of Perelman," J. GT , math. Bill Thurston , who made fundamental contributions to our understanding of low-dimensional manifolds and related structures, died on Tuesday , aged This difficult theorem connecting the topological and geometric structure of 3-manifolds led Thurston to give his influential geometrisation conjecture , which in principle, at least completely classifies the topology of an arbitrary compact 3-manifold as a combination of eight model geometries now known as Thurston model geometries.

geometrization

In addition to his direct mathematical research contributions, Thurston was also an amazing mathematical expositor, having the rare knack of being able to describe the process of mathematical thinking in addition to the results of that process and the intuition underlying it. I unfortunately never had the opportunity to meet Thurston in person although we did correspond a few times online , but I know many mathematicians who have been profoundly influenced by him and his work. His death is a great loss for mathematics. AT , math.

The geometry of 3-manifolds

DG , math. GT Tags: 3-manifolds , geometrization conjecture , Poincare conjecture , spherical space form , surgery by Terence Tao 16 comments. Theorem 1.

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Then M is homeomorphic to a 3-sphere. I will take it for granted that this result is of interest, but you can read the Notices article of Milnor , the Bulletin article of Morgan , or the Clay Mathematical Institute description of the problem also by Milnor for background and motivation for this conjecture. On the other hand, the geometrisation conjecture will be rather visibly lurking beneath the surface in the discussion of this lecture.


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  • Create a free website or blog at WordPress. Ben Eastaugh and Chris Sternal-Johnson. Subscribe to feed. What's new Updates on my research and expository papers, discussion of open problems, and other maths-related topics. Tag Archive. Bill Thurston 22 August, in math.

    Geometrization of 3-Orbifolds of Cyclic Type

    At the risk of belaboring the obvious, here is the statement of that conjecture: Theorem 1. What is good mathematics? Why global regularity for Navier-Stokes is hard.