Sewing symplectic volumes for flat connections over compact surfaces (Q1970237)

Let \(\Sigma\) be a closed oriented connected surface which may be decomposed into compact oriented surfaces \(\Sigma _1\) and \(\Sigma _2 \) sewn along a common connected boundary \(\partial \Sigma_i\). The auhor derives a formula which expresses the symplectic volume measure on the moduli space of flat connection over \(\Sigma\) in terms of the corresponing volume measures for the surfaces \(\Sigma _1\) and \(\Sigma _2 \).