2023/11/09 by Absos Ali Shaikh, Shaikh, Absos Ali, Uddhab Roy +1
Computer Science · Mathematics · Physics and Astronomy · #20H10 #30F35 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Theoretical and Computational Physics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2311.07501
openalex publication_date 2023/11/09 · openalex created_date 2023/11/15 · openalex updated_date 2026/07/28
The goal of this article is to initiate the study of estimates of the non-classical Schottky structure in the discrete subgroups of the projective special linear group over the real numbers degree 2. In fact, in this paper, we have investigated the non-classical generating sets in the Fuchsian Schottky groups on the hyperbolic plane with boundary. A Schottky group is usually considered non-classical if the curves used in the Schottky construction are Jordan curves (except the Euclidean circles). More precisely, in this manuscript, we have provided a structure of the rank 2 Fuchsian Schottky groups with non-classical generating sets by utilizing two suitable hyperbolic Möbius transformations on the upper-half plane model. In particular, we have derived two non-trivial examples of Fuchsian Schottky groups with non-classical generating sets in the upper-half plane with the circle at infinity as the boundary.