Ricci flow and the Poincaré Conjecture
Math 538, Spring 2009

Instructor: David Glickenstein
Office: Mathematics 715
Office Phone: 621-2463
Email: glickenstein@math.arizona.edu

Notes

• All notes from the class.
  
• First batch: Introduction to the Poincaré conjecture (updated 1/20/2009)
• Second batch: Quick introduction to Riemannian geometry (updated 1/20/2009)
• Third batch: Introduction to flows on Riemannian manifolds (updated 2/5/2009)
• Fourth batch: Introduction to the maximum principle (updated 2/10/2009)
• Fifth batch: Singularities of Ricci flow, limits, and κ-noncollapse (updated 2/18/2009)
• Sixth batch: Perelman's entropy and κ-noncollapse (updated 3/5/2009)
• Batch 6.5: What is going on with the program (updated 3/12/2009)
• Batch 7: Reduced distance and volume (updated 4/14/2009)
• Batch 7.5: More on derivatives of distance.
  

Problems

• Problems on kappa-noncollapse and Perelman's F and W functionals.

Reference and Supplementary material

• Ricci flow and the Poincaré Conjecture, by J. Morgan and G. Tian. Preprint version is also available here.
• Completion of the Proof of the Geometrization Conjecture, by J. Morgan and G. Tian.
• A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow, by H.-D. Cao and X.-P. Zhu. There are also errata for this paper.
  
• Notes on Perelman's papers, by B. Kleiner and J. Lott.
  
• The Ricci flow: An Introduction, by B. Chow and D. Knopf.
• Hamilton's Ricci flow, by B. Chow, P. Lu, and L. Ni.
• The Ricci flow: Techniques and Applications, Parts I and II, by B. Chow et al.