Bolza-like surfaces in the Thurston set
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912324892229632 |
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| author | Dey, Achintya Saha, Bhola Nath Sanki, Bidyut |
| author_facet | Dey, Achintya Saha, Bhola Nath Sanki, Bidyut |
| contents | A surface in the Teichmüller space, where the systole function admits its maximum, is called a maximal surface. For genus two, a unique maximal surface exists, which is called the Bolza surface, whose systolic geodesics give a triangulation of the surface. We define a surface as Bolza-like if its systolic geodesics decompose the surface into $(p, q, r)$-triangles for some integers $p,q,r$. In this article, we will provide a construction of Bolza-like surfaces for infinitely many genera $g\geq 9$. Next, we see an intriguing application of Bolza-like surfaces. In particular, we construct global maximal surfaces using these Bolza-like surfaces. Furthermore, we study a symmetric property satisfied by the systolic geodesics of our Bolza-like surfaces. We show that any simple closed geodesic intersects the systolic geodesics at an even number of points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_09483 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Bolza-like surfaces in the Thurston set Dey, Achintya Saha, Bhola Nath Sanki, Bidyut Geometric Topology A surface in the Teichmüller space, where the systole function admits its maximum, is called a maximal surface. For genus two, a unique maximal surface exists, which is called the Bolza surface, whose systolic geodesics give a triangulation of the surface. We define a surface as Bolza-like if its systolic geodesics decompose the surface into $(p, q, r)$-triangles for some integers $p,q,r$. In this article, we will provide a construction of Bolza-like surfaces for infinitely many genera $g\geq 9$. Next, we see an intriguing application of Bolza-like surfaces. In particular, we construct global maximal surfaces using these Bolza-like surfaces. Furthermore, we study a symmetric property satisfied by the systolic geodesics of our Bolza-like surfaces. We show that any simple closed geodesic intersects the systolic geodesics at an even number of points. |
| title | Bolza-like surfaces in the Thurston set |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2504.09483 |