Seminar on foundations in 3-manifold topology
We study foundational topics in 3-manifold topology: Normal surfaces, incompressible surfaces, Waldhausen's result that Haken manifolds are classified by their fundamental group, geometric structures on 3-manifolds, Seifert fibered 3-manifolds, and some other results.
The seminar meets on Tuesdays 2-4pm in M311. The first meeting is on Thursday, 25.4.19 from 2-4pm in M311.
We mainly use the following literature- [M] B. Martelli "An Introduction to Geometric Topology", available on the arXiv
- [H] J. Hempel, "3-manifolds", AMS Chelsea
- [S] P. Scott, "The geometries of 3-manifolds", Bull. London Math. Soc, 15 (1983), 401--487
- [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
| Date | Topic | Speaker | Literature |
|---|---|---|---|
| 30.4. | Normal surfaces and incompressible surfaces | Raphael Zentner | [M, Chap. 9] |
| 7.5. | Kneser's theorem on prime decompositions | Raphael Zentner | [M, Chap. 9] |
| 14.5. | Kneser's theorem on prime decompositions, continued | Raphael Zentner | [M, Chap. 9] |
| 28.5. | Nielsen's theorem on π1-injective maps between surfaces | Gerrit Herrmann | [H, Chap 13] |
| 4.6. | Waldhausen's theorem for 3-manifolds which are "sufficiently large" | Gerrit Herrmann | [H, Chap 13] |
| 25.6. | The Gromov norm | Marco Moraschini | |
| 28.6. | Mostow's rigidity theorem | Marco Moraschini | |
| 9.7. | Seifert fibered 3-manifolds and geometric structures on 3-manifolds, I | Damian Itgen | [S] |
| 16.7. | The Lickorish-Wallace theorem | Giacomo Bascape | |
| 23.7. | Seifert fibered 3-manifolds and geometric structures on 3-manifolds, II | Felix Eberhart | [S] |