Topology Seminar Fall 2006

The topic for the fall semester, perhaps continuing into the spring will be Thurston's hyperbolization theorem. The plan is to go through J. P. Otal's paper, Thurston's hyperbolization of Haken Manifolds, in Surveys on Differential Geometry III (International Press, 1998). We will fill in background material from some of the references given below. We will also try to understand the statement of the Geometrization Theorem, which has been proved by Perel'man using Hamilton's theory of Ricci flow.

There will also be occasional talks by outside speakers, to be announced.

For the schedule, please consult the Current Brandeis Mathematics Calendar, which displays all future talks and events. You can also consult the new Seminar page.

References on hyperbolic geometry:

• J. P. Otal, Thurston's hyperbolization of Haken Manifolds, in Surveys on Differential Geometry III (International Press, 1998).
• John Ratcliffe, Foundations of hyperbolic manifolds (Springer-Verlag, 1994).
• William P. Thurston, Three-dimensional geometry and topology (Princeton University Press, 1997).
• John Hempel, 3-Manifolds, Annals of Math. Studies 86 (Princeton University Press, 1976).
• R. Benedetti and C. Petronio, Lectures on Hyperbolic Geometry (Springer-Verlag, 1992).

References on geometrization:

• Peter Scott, The geometries of 3-manifolds, Bull. Lond. Math. Soc. 15 (1983), 401-487.
• Three papers of G. Perel'man on the math arxiv:
  1. The entropy formula for the Ricci flow and its geometric applications
  2. Ricci flow with surgery on three-manifolds
  3. Finite extinction time for the solutions to the Ricci flow on certain three-manifolds
• John Morgan and Gang Tian, Ricci Flow and the Poincare Conjecture
• Huai-Dong Cao and Xi-Ping Zhu, A Complete Proof of the Poincaré and Geometrization Conjectures - Application of the Hamilton-Perelman theory of the Ricci flow, Asian J. Math. 10 (June 2006).