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Yang-Mills Theory over Riemann Surfaces and the Atiyah-Segal Theorem
Student-Run Geometry/Topology Seminar| Speaker: | Daniel Ramras, Stanford University |
| Location: | 2112 MSB |
| Start time: | Thu, Jan 11 2007, 1:10PM |
Given a representation f:G --> U(n), one can form a vector bundle over the classifying space BG via the mixing construction. When G is a compact Lie group, the Atiyah-Segal theorem uses this construction to provide a precise relationship between the representation ring R[G] and the topological K-theory of BG. In this talk, I'll explain how Yang-Mills theory over a Riemann surface S can be used to prove an analogous theorem relating representations of \pi_1(S) to K*(S). Along the way, I'll explain the Yang-Mills functional on the space of connections, and how Morse-theoretical techniques may be applied to it.