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Yayın Gluing formulas for volume forms on representation varieties of surfaces(Springer Nature, 2025-08-06) Erdal, Esma DiricanLet Σg,n be a compact oriented surface of genus g≥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 π1(Σg,0) in any semi-simple Lie group. In the present paper, we first obtain a multiplicative gluing formula for the twisted Reidemeister torsion of Σg,0 in terms of torsions of Σg1,1,Σg2,1, and boundary circle S1, where g=g1+g2 and g1,g2≥2. Then, by using Heusener and Porti’s results on Σg,n, we show that the symplectic volume form on the representation variety of Σg,0 can be expressed as a product of the holomorphic symplectic volume forms on the relative representation varieties of surfaces Σg1,1 and Σg2,1.Yayın On twisted torsion of compact 3-manifolds(Cornell Univ, 2024-08-20) Erdal, Esma DiricanLet M be a 3-manifold with connected non-vacuos boundary which is not spherical. Assume that N is another 3-manifold with vacuous boundary and N∗ is the 3-manifold obtained by removing from N the interior of a 3-cell. In the present paper, we find a relationship between the multiplicative property of the twisted Reidemeister torsion and the connected sum operation on these manifolds in order to understand their topology and geometry.
