Voorjaarssemester 1999

**Reading Seminar for students, Mondays, 16.00-17.30, room WI 401, begin: 18th January**

The plan of this seminar is to read together through the book **Lectures on Seiberg-Witten Invariants** by J.D. Moore (on reserve in the reading room of our library). Each student who wants to receive credit for this seminar (7 study points) has to give one of the fourteen 90 minute talks. Graduate students and staff are very welcome to attend and to participate actively by giving talks not distributed among students. As background knowledge a first course on manifolds should suffice. Vector bundles and connections will be reviewed in the first talk. A knowledge of homology theory, as developed in my course **Introduction to Geometric and Algebraic Topology** will be useful and at certain points essential, but I hope that this and all other necessary background material can be picked up during the seminar.

During the 1980's, Simon Donaldson used methods originating from mathematical physics (Yang-Mills equations) to prove remarkable theorems about the topology of 4-manifolds (winning him a Fields medal in 1986) of the following type:

- There exist topological 4-manifolds without differentiable structure.
- There exist differential 4-manifolds which are homeomorphic but not diffeomorphic.

Date |
Title |
Chapter |
see also |
Speaker |

18.01. |
Vector bundles and connections | 1.2, 1.3 |
[MS] | Koos van Winden |

25.01 |
Curvature of connections, characteristic classes | 1.4, 1.5 |
[H] | Hansjörg Geiges |

01.02 |
The universal bundle | 1.6 |
[MS] | Gerben Dirksen |

08.02 |
No seminar (Dies Natalis) | |||

15.02 |
Classification of connections | 1.7 |
Otto van Koert | |

22.02 |
Hodge theory | 1.8 |
[W] | Willem van Briemen |

01.03 |
Spin-, Spin^{c}- and almost complex structures |
2.1-2.3 |
Bernard Meulenbroek | |

08.03 |
Clifford algebras | 2.4 |
[LM] | Otto van Koert |

15.03 |
The Spin-connection | 2.5 |
[LM] | Bob Planqué |

22.03 |
The Dirac-operator | 2.6 |
[LM] | Erdal Emsiz |

12.04 |
The Atiyah-Singer index theorem | 2.7 |
[LM] | Erik van Erp |

19.04 |
The Seiberg-Witten equations and compactness of the moduli space | 3.1-3.3 |
Raoul Pietersz | |

26.04 |
Transversality | 3.4 |
Christoph Hummel | |

03.05 |
Topology of 4-manifolds | 3.5 |
Hansjörg Geiges | |

10.05 |
Seiberg-Witten invariants and Dirac operator on Kähler surfaces | 3.6, 3.7 |
Martin Lübke |

[H] | D. Husemoller: | Fibre bundles, 3^{rd}ed., Springer, 1994. |
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[LS] | H. Lawson, M. Michelson: | Spin Geometry, Princeton Univ. Press, 1989. |
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[MS] | J. Milnor, J. Stasheff: | Characteristic Classes, Princeton Univ. Press, 1974. |
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[W] | F. Warner: | Foundations of differentiable manifolds and Lie groups, Springer, 1983. |

For further information and assistance in preparing your talks you may contact

, or .