Donaldson and Seiberg-Witten Invariants: The Witten Conjecture

Gregory Naber

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Submission date: 25. Jul. 2005
Pages: 287
Bibtex

Abstract:
The Donaldson invariants of a smooth 4-manifold M are subtle probes into the differential topological structure of M. They are defined from the structure of a moduli space of solutions to certain partial differential equations proposed by physicists (Yang-Mills) to model the interactions between elementary particles. Edward Witten found that they can also be regarded as expectation values for certain observables in a topological quantum field theory (TQFT). His insight into the physics of this TQFT (based on joint work with Nathan Seiberg) led him to conjecture that the information contained in the Donaldson invariants can also be retrieved from a much simpler set of equations (Seiberg-Witten). The impact of this conjecture, still not fully proved, but surely "true", has been spectacular. The rather modest objective of these lectures is to provide the background required to understand what the conjecture says.Download lecture slides and addendums

• Lecture 1: PDF, 417 kB
• Lectures 2 and 3: PDF, 670 kB
• Lecture 4: PDF, 635 kB
• Addendum 1: PDF, 260 kB
• Addendum 2: PDF, 226 kB
• Addendum 3: PDF, 55 kB
• Addendum 4: PDF, 83 kB
• Addendum 5: PDF, 242 kB
• Addendum 6: PDF, 179 kB
• Addendum 7: PDF, 172 kB
• Addendum 8: PDF, 1480 kB
• Addendum 9: PDF, 429 kB
• Addendum 10: PDF, 394 kB
• Addendum 11: PDF, 383 kB
• Addendum 12: PDF, 2490 kB
• Addendum 13: PDF, 1865 kB
• Addendum 14: PDF, 1687 kB
• Addendum 15: PDF, 599 kB
• Addendum 16: PDF, 1044 kB
• Addendum 17: PDF, 287 kB