Hauptseminar Symplektische Geometrie

In Yang-Mills theory, many important properties of the physical system are encoded in the structure of the moduli space of connections with respect to the group of gauge transformations. Atiyah and Bott studied this moduli space in their seminal paper by using symplectic reduction adapted to the special case of a Riemann surface as the base manifold. The functional analytic problems were approached using Sobolev space techniques. In this talk, I will show how these results can be extended and reformulated in the framework of Fréchet manifolds. In the spirit of reduction by stages, we first take the quotient by the free action of based gauge transformations and in the second step consider the singular action by the finite-dimensional residual group. In particular, central Yang-Mills connections are realized as a subset of the Fréchet manifold of based gauge equivalence classes of connections and are identified as the inverse image under the Wilson holonomy loop map.

Mittwoch, den 24. Januar 2018 um 16.15 Uhr, in Mathematikon, INF 205, SR 4 Mittwoch, den 24. Januar 2018 at 16.15, in Mathematikon, INF 205, SR 4

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. P. Albers