Math 276 - Section 1 -
Topics in Topology
Instructor: Ian Agol
9:30-11:00am, Room 51 Evans
Course Control Number: 54758
Office: 921 Evans
Office Hours: TBA
Class will be cancelled T/Th Jan. 26,
28, because of MSRI meeting
On Thursday, February 18, Ken Bromberg will give a guest lecture
on Dehn surgeries on the figure 8 knot complement.
Class will be cancelled April 20 & 22.
We will probably have some make-up classes May 4 & 6 during the
Prerequisites: Algebraic Topology, Riemannian Geometry, would
be helpful to have attended Math 277 fall 2009.
Required Text: There will be
notes made available over the
course of the semester.
Due 2/2/10: Go through chapter 3 of Kirby's problem list,
and determine which problems
follow as consequences of the geometrization or orbifolds theorems.
Due 2/9/10: Classify covers with cyclic fundamental group of
closed aspherical 3-manifolds
Due 2/16/10: Describe the geometric decomposition and a non-positively
curved Riemannian metric with
locally Euclidean geodesic boundary on the 4 chain link complement.
Peter Scott, The
geometries of 3-manifolds
William Thurston, Three-dimensional Geometry and Topology, Vol. 1.
Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton
University Press, Princeton, NJ, 1997. x+311 pp. ISBN 0-691-08304-5.
preliminary draft book (12.2 MB scanned copy)
Cooper, Daryl; Hodgson, Craig D.; Kerckhoff, Steven P.
Three-dimensional Orbifolds and Cone-manifolds. With a Postface by
Sadayoshi Kojima, MSJ Memoirs, 5. Mathematical Society of Japan, Tokyo,
2000. x+170 pp. ISBN 4-931469-05-1.
Boileau, Maillot, Porti, Three
dimensional orbifolds and their geometric structures
Boileau, Leeb, Porti, Geometrization
on the proof of Geometrization using Ricci flow
Geometrization conjecture and universal covers of 3-manifolds
talk at the Cornell Topology Festival, 2004
lectures on homeomorphism classification of 3-manifolds
Three-dimensional manifolds (Graduate Course, Michaelmas 1999)
Notes on basic 3-manifold topology
Geometry and Topology of 3-manifolds
Syllabus: This seminar will
focus on topics in 3-manifold
topology which are consequences of the Geometrization Theorem and
Orbifold Theorem, which we will take for the most part as a black box.
Some topics may include:
- review of Thurston's 8 geometries and the geometrization and orbifold
- classification of universal covers of closed 3-manifolds
- geometric proofs of Dehn's lemma, the loop theorem, and sphere theorem
- homotopy rigidity of aspherical 3-manifolds
- solution to the word and conjugacy problems in 3-manifold fundamental
- algorithmic classification of compact 3-manifolds
- homotopy equivalence classficiation, and simply homotopy equivalence
=> homeomorphic for closed 3-manifolds
If there is time, we may survey some other topics such as the
classification of covers of compact 3-manifolds with finitely generated
fundamental group, the generalized Smale conjecture, Dehn surgery
results, and volume estimates for Haken hyperbolic 3-manifolds.