Finite and infinite degree Thurston maps with a small postsingular set
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914962453037056 |
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| author | Prochorov, Nikolai |
| author_facet | Prochorov, Nikolai |
| contents | We develop the theory of Thurston maps that are defined everywhere on the topological sphere $S^2$ with a possible exception of a single essential singularity. We establish an analog of the celebrated W. Thurston's characterization theorem for a broad class of such Thurston maps having four postsingular values. To achieve this, we analyze the corresponding pullback maps defined on the one-complex dimensional Teichmüller space. This analysis also allows us to derive various properties of Hurwitz classes of the corresponding Thurston maps. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_01146 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Finite and infinite degree Thurston maps with a small postsingular set Prochorov, Nikolai Dynamical Systems Geometric Topology Primary 37F20, Secondary 37F10, 37F15, 37F34 We develop the theory of Thurston maps that are defined everywhere on the topological sphere $S^2$ with a possible exception of a single essential singularity. We establish an analog of the celebrated W. Thurston's characterization theorem for a broad class of such Thurston maps having four postsingular values. To achieve this, we analyze the corresponding pullback maps defined on the one-complex dimensional Teichmüller space. This analysis also allows us to derive various properties of Hurwitz classes of the corresponding Thurston maps. |
| title | Finite and infinite degree Thurston maps with a small postsingular set |
| topic | Dynamical Systems Geometric Topology Primary 37F20, Secondary 37F10, 37F15, 37F34 |
| url | https://arxiv.org/abs/2410.01146 |