On the Connectedness of Moduli Spaces of Flat Connections over Compact Surfaces Nan-kuo Ho and Chiu-chu
نویسنده
چکیده
We know that there is an isomorphism between the moduli space of gauge equivalence classes of flat G-connections on a compact surface and the moduli space of representations from the fundamental group of the surface to G acted on by the adjoint action (cf: Goldman[G]). It is known that if G is compact, semi-simple and simply connected, the moduli space of gauge equivalence classes of flat G-connections on a compact orientable surface is connected. (The fibers of the moment map for a compact, connected, group valued Hamiltonian space are connected provided the group is simply connected, cf:[AMM]). Thus it is natural to ask about the connectedness of the moduli space of gauge equivalence classes of flat G-connections on a compact nonorientable surface.
منابع مشابه
Connected Components of Spaces of Surface Group Representations Ii Nan-kuo Ho and Chiu-chu
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