Mini-course at MIT : Selected topics in 3-manifold topology
We discuss classical topics in 3-manifold topology: Normal surfaces, incompressible surfaces, Dehn's Lemma and the Loop Theorem, hierarchies. Applications will cover Waldhausen's result that Haken manifolds are classified by their fundamental group, and some other results.
The course is usually mondays 4:15 -- 4:30-ish at MIT, until the end of the term, but precise dates vary a bit due to some double header of the previous geometry seminar, and holidays etc. There is a mailing list for short term announcements, but I will also try to keep this page up to date. Please email me if you are interested.
We mainly use the following Literature- [L] M. Lackenby, "Lecture notes on 3-manifolds", available on M. Lackenby's homepage
- [M] B. Martelli "An Introduction to Geometric Topology", available on the arXiv
- [H] J. Hempel, "3-manifolds", AMS Chelsea
- [W] F. Waldhausen, "On irreducible 3-manifolds which are sufficiently large", Annals of Mathematics, Second Series, Vol. 87, No. 1 (Jan., 1968), pp. 56--88
- [AFW] M. Aschenbrenner, S. Friedl, H. Wilton, "3-Manifold Groups", EMS Series of Lectures in Mathematics
| Date and Time | Room | Topic | Literature |
|---|---|---|---|
| Mo 10/22 4:15 | MIT 4-231 | Normal surfaces, finiteness result | [M, Chap. 9.2] |
| We 10/31 4:00 | MIT 2-449 | The Prime Decomposition Theorem, incompressible surfaces I | [M, Chap. 9.2 and 9.3] |
| Mo 11/5 4:15 | MIT 4-231 | Incompressible surfaces II, Haken manifolds I, Example: The Whithead double of the figure eight knot | [M, Chap. 9.3 and 9.4] |
| We 11/14 4:00 | MIT 2-190 | Haken manifolds II, hierarchies, Examples of hierarchies | [M, Chap. 9.3 and 9.4] and [H, Chap 13] |
| Mo 11/19 4:15 | MIT 4-231 | Hierarchies, the Loop theorem, and applications | [L,Chap. 8--11] |
| Mo 11/26 4:15 | MIT 4-231 | Boundary patterns, proof of the Loop theorem using hierarchies | [L,Chap. 8--11] |
| We 11/28 4:00 | MIT 2-449 | Enf of proof of Loop theorem, Waldhausen's theorem I | [L,Chap. 8--11], [L,Chap. 12], [H, Chap 13], [W] |
| Mo 12/3 4:15 | MIT 4-231 | Waldhausen's theorem II | [L,Chap. 12], [H, Chap 13], [W] |
| We 12/5 4:00 | MIT 2-449 | Waldhausen's theorem III | [L,Chap. 12], [H, Chap 13], [W] |
| We 12/12 9:15 | MIT 2-449 | JSJ-decomposition, the geometric decomposition, Thurston's geometrization conjecture, Perelman's results, π1-classification results | [AFW,Chap. 1], [L,Chap. 12], [H, Chap 13], [W] |