Let \(\Sigma _{g,n}\) be a compact oriented surface of genus \(g\ge 4\) with n boundary components. Due to Witten, the twisted Reidemeister torsion coincides with a power of the Atiyah–Bott–Goldman–Narasimhan symplectic form on the space of representations of \(\pi _1(\Sigma _{g,0})\) in any semi-simple Lie group. In the present paper, we first obtain a multiplicative gluing formula for the twisted Reidemeister torsion of \(\Sigma _{g,0}\) in terms of torsions of \(\Sigma _{g_1,1},\) \(\Sigma _{g_2,1},\) and boundary circle \(\mathbb {S}^1,\) where \(g=g_1+g_2\) and \(g_1, g_2\ge 2.\) Then, by using Heusener and Porti’s results on \(\Sigma _{g,n},\) we show that the symplectic volume form on the representation variety of \(\Sigma _{g,0}\) can be expressed as a product of the holomorphic symplectic volume forms on the relative representation varieties of surfaces \(\Sigma _{g_1,1}\) and \(\Sigma _{g_2,1}.\)
