MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

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Funded by The Danish National Research Foundation

Geometric Mathematical Physics Seminar

Abstract
In this talk we give an introduction to Seiberg-Witten theory on 3-manifolds based on the work of Y. Lim [Seiberg-Witten invariants for 3-manifolds in the case b_1=0 or 1, Pacific J. Math. 195 (2000)] and W. Chen [Casson's invariant and Seiberg-Witten gauge theory, Turkish J. Math. 21 (1997)]. The Seiberg-Witten equations are interpreted as critical point equations of the Chern-Simons-Dirac functional. Viewing the latter as a Morse function, we define the Seiberg-Witten invariant as the Euler characteristic of the configuration space modulo gauge equivalence. We then analyse its behaviour under deformation of the Riemannian metric in order to obtain a topological invariant. For rational homology spheres, this can only be achieved by modifying the Seiberg-Witten invariant by a combination of eta-invariants.

Contact person:Jørgen Ellegaard Andersen.