2021/10/18 by Absos Ali Shaikh, Shaikh, Absos Ali, Uddhab Roy +1
Computer Science · Materials Science · Mathematics · #20H10 #30F35 #30F40 #37F32 #57K20 #Differential Geometry (math.DG) #Digital Image Processing Techniques #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Quasicrystal Structures and Properties
paper · pdf · doi:10.48550/arxiv.2110.13263
openalex publication_date 2021/10/18 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this article, we have constructed an interesting type of generalized\nSchottky group, named as Fuchsian Schottky group of arbitrary finite rank, in\nthe context of the classical Schottky group (i.e., Schottky curves which are\nEuclidean circles). After that, we initiated the construction of the\ngeneralized Fuchsian Schottky group of any finite rank by including\norientation-reversing isometries of the hyperbolic plane as side-pairing\ntransformations. Further, we have investigated the hyperbolic ends for any\narbitrary finite rank Fuchsian Schottky groups from the point of view of the\nEuler characteristic in the hyperbolic surface. Finally, we have shown that the\ncompact core of the conformally compact Riemann surface can be decomposed into\nnon-tight pairs of pants by using suitable twist parameters with some fixed\nBers' constant. The Fenchel-Nielsen coordinates for Teichm "uller space\ncorresponding to any finite rank Fuchsian Schottky groups are also obtained.\n