**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**] |