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Öğe A Note on Representation Variety of Abelian Groups and Reidemeister Torsion(Springer, 2021) Hezenci, F.; Sozen, Y.Let 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.Öğe On bitsadze-samarskii type elliptic differential problems on hyperbolic plane(Academic Publications Ltd., 2021) Ashyralyev, A.; Sozen, Y.; Hezenci, F.In the present article, we consider nonlocal boundary value problems (NBVP) of elliptic type on relatively compact domains in the hyperbolic plane. We establish the wellposedness of Neumann-Bitsadze-Samarskii type and also Dirichlet-Bitsadze-Samarskii type on such domains. Furthermore, we establish new coercivity inequalities for solutions of such elliptic NBVP on relatively compact domains in the hyperbolic plane with various H¨older norms. © 2021Öğe A remark on elliptic differential equations on manifold(Karaganda State Univ, 2020) Ashyralyev, A.; Sozen, Y.; Hezenci, F.For elliptic boundary value problems of nonlocal type in Euclidean space, the well posedness has been studied by several authors and it has been well understood. On the other hand, such kind of problems on manifolds have not been studied yet. Present article considers differential equations on smooth closed manifolds. It establishes the well posedness of nonlocal boundary value problems of elliptic type, namely Neumann-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds and also Dirichlet-Bitsadze-Samarskii type nonlocal boundary value problem on manifolds, in Holder spaces. In addition, in various Holder norms, it establishes new coercivity inequalities for solutions of such elliptic nonlocal type boundary value problems on smooth manifolds.Öğe A remark on Schottky representations and Reidemeister torsion(Karaganda State Univ, 2023) Hezenci, F.; Sozen, Y.The present paper establishes a formula of Reidemeister torsion for Schottky representations. The theoretical results are applied to 3-manifolds with boundary consisting orientable surfaces with genus at least 2.
