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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2311.07501 |
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| _version_ | 1866917061865766912 |
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| author | Shaikh, Absos Ali Roy, Uddhab |
| author_facet | Shaikh, Absos Ali Roy, Uddhab |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_07501 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Non-classical generating sets in Fuchsian Schottky groups Shaikh, Absos Ali Roy, Uddhab Differential Geometry 20H10, 30F35 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. |
| title | Non-classical generating sets in Fuchsian Schottky groups |
| topic | Differential Geometry 20H10, 30F35 |
| url | https://arxiv.org/abs/2311.07501 |