Advanced topics in geometry: Ricci flow
Fall 2009

Bruce Kleiner



Location: Thursdays 9:30-11:20am, 512 WWH.


References
3-manifolds:
  • Lectures on 3-manifold topology,  W. Jaco.
  • 3-manifolds, J. Hempel
Thurston's Geometrization Conjecture:
  • "The geometries of 3-manifolds",  P. Scott, Bull. LMS, 1983.
  • Three-dimensional Geometry and Topology, Vol. 1, W. Thurston, Princeton.
Riemannian Geometry:
  • Comparison theorems in Riemannian Geometry, J. Cheeger and D. Ebin.
  • Riemannian Geometry, Do Carmo.
  • M. L. Gromov, Metric structures for Riemannian and non-Riemannian spaces, Progr. Math., 152, Birkhäuser, 1999.
  • A course in metric geometry, D. Burago and S. Ivanov, Graduate studies in Mathematics, 33, AMS, 2001.
  • "Volume collapsed three-manifolds with a lower curvature bound", T. Shioya and T. Yamaguchi, math.DG/0304472
Ricci flow surveys:
  • "Recent progress on the Poincaré conjecture and the classification of 3-manifolds," J. Morgan, BAMS, (2005).
  • "Towards the Poincaré conjecture and the classification of 3-manifolds," J. Milnor, Notices AMS, 2003.
  • "Geometrization of 3-manifolds via the Ricci flow," M. Anderson, Notices AMS, 2004.
    • "Overview of Perelman's papers on Ricci flow", B. Kleiner and J. Lott, ps
Ricci flow sources:
  • Lectures on the Ricci flow, Peter Topping, L.M.S. Lecture note series 325 C.U.P. (2006) pdf.
  • The Ricci flow: an introduction, B. Chow and D. Knopf, Mathematical surveys and Monographs, AMS, 2004.
  • 2005 MSRI summer school Ricci flow videos.
  • "Three-manifolds with positive Ricci curvature," R. Hamilton, J. Diff. Geom.,  17 (1982), no. 2, 255--306.
  • "Four-manifolds with positive curvature operator", R. Hamilton,  Diff. Geom.,  24 (1986), no. 2, 153--179.
  • "The formation of singularities in the Ricci flow," R. Hamilton, Surveys in differential geometry, Vol. II (Cambridge, MA, 1993), 7--136, Internat. Press, Cambridge, MA, 1995.
  • "Non-singular solutions of the Ricci flow on three-manifolds", R. Hamilton, Comm. Anal. Geom, 7, 1999, no.4, 695-729.
  • "The entropy formula for Ricci flow and its geometric applications," G. Perelman, math.DG/0211159.
  • "Ricci flow with surgery on three-manifolds", G. Perelman, math.DG/0303109.
  • Website for material related to Perelman's work.  Click here