Hezenci, F.Sozen, Y.2021-12-012021-12-012021978303069291921941009https://doi.org/10.1007/978-3-030-69292-6_13https://hdl.handle.net/20.500.12684/99184th International Conference on Analysis and Applied Mathematics, ICAAM 2018 -- 6 September 2018 through 9 September 2018 -- -- 262329Let S and G denote respectively the 2 - torus and one of the Lie groups GL (n, C), SL (n, C), SO (n, C), Sp (2 n, C). In the present article, we consider the smooth part of the representation variety Rep (S, G) consisting of conjugacy classes of homomorphisms from fundamental group ?1(S) to G. We show the well definiteness of Reidemeister torsion for such representations. In addition, we establish a formula for computing the Reidemeister torsion of such representations in terms of the symplectic structure on Rep (S, G) [51]. This symplectic form is analogous to Atiyah–Bott–Goldman symplectic form of higher genera for the Lie group G. © 2021, Springer Nature Switzerland AG.en10.1007/978-3-030-69292-6_13info:eu-repo/semantics/closedAccessAbelian varietiesAtiyah-Bott-Goldman Symplectic FormChain complexReidemeister torsionRepresentation varietiesSymplectic chain complexConference Object3511711812-s2.0-85112195940N/A