# University of Toronto's Symplectic Geometry Seminar

March 10, 2003, 2pm

SS5017A

## Nan-kuo Ho

###
Toronto

##
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.