Nr. | Date | Topics | Notes | References |
01. | Mon. 28/1 | Topological spaces, topological manifolds, homotopy groups. | | [Bre], [May] |
02. | Fri. 1/2 | The fundamental group and groupoid, the universal cover, higher homotopy groups. | * | [Bre], [May] |
03. | Mon. 4/2 | Computations, simplicial complexes, triangulations. | | [Bre], [May], [Arm] |
04. | Mon. 11/2 | Principal bundles, long exact sequences of homotoy groups. | | [Hus], [Bre], [May] |
05. | Wed. 13/2 | Homotopy lifting property and examples. | | [Bre], [May] |
06. | Fri. 1/3 | More examples of principal bundles, classifying spaces. | | [Hus] |
07. | Tue. 5/3 | The Poincaré homology sphere, classification of principal bundles. | | [Hus] |
08. | Mon. 11/3 | Introduction to knot theory. Smooth manifolds. | | [Mil] |
09. | Thu. 14/3 | The isotopy extension theorem. Knot projections and knot diagrams. | | [Kos], [Bur] |
10. | Mon. 18/3 | Reidemeister moves, the Quandle invariant. | | [Bur], [Man] |
11. | Thu. 21/3 | Linking numbers, surfaces with and without boundary | | [Man], [Arm] |
12. | Mon. 25/3 | Seifert surfaces, connected sum | * | [Man] |
13. | Tor. 28/3 | Connected sum, Intersection form, Seifert matrix, Alexander polynomial | | [Arm],[Bur] |
14. | Fri. 5/4 | Finitely presented groups, the Braid group | | [Man] |
15. | Mon. 8/4 | Jones polynomial, Seifert van Kampen theorem, the knot group, the Wirtinger representation | | [Man],[Bre] |
16. | Tue. 7/5 | Tangent bundle, Lie bracket, de Rham complex. | | [Bot] |
17. | Fri. 10/5 | Integration of forms, Lie groups, Adjoint representation | | [Bot],[Kos] |
18. | Tue. 14/5 | Cartan one-form, Maurer-Cartan equation, Ehresmann connection | | [Son] |
19. | Fri. 24/5 | S1-bundles, Parallel transport, Monodromy (holonomy) | | [Son] |
20. | Tue. 28/5 | Flatness, curvature, Gauss-Bonnet theorem | | [Son] |