University of Toronto's Symplectic Geometry Seminar

March 10, 2003, 2pm

Nan-kuo Ho


Connected components of moduli spaces of flat connections over compact nonorientable surfaces

Abstract: Let G be a connected, compact, semisimple Lie group. It is known that the number of connected components of the moduli space of gauge equivalence classes of flat G-connections over a closed orientable Riemann surface S of genus bigger than 2 is equal to the order of H^2(S,\pi_1(G)). We show that the same statement for a compact closed nonorientable surface S which is homeomorphic to the connected sum of k copies of the real projective plan, where k \neq 1,2,4, can be easily derived from a result in A,Alekseev,A.Malkin, and E.Meinrenken's recent work on Lie group valued moment maps. This is joint work with Chiu-Chu Melissa Liu.