Definition 5

The space of flat connections on a decorated Riemann surface ℑ g , n subscript 𝑔 𝑛 \Im_{g,n} roman_ℑ start_POSTSUBSCRIPT italic_g , italic_n end_POSTSUBSCRIPT is defined as a space of solutions of the following equation which replaces the zero curvature condition:

μ ⁢ ( z ) = 0 . 𝜇 𝑧 0 \mu(z)=0. italic_μ ( italic_z ) = 0 . (2.16)