Finite and infinite degree Thurston maps with a small postsingular set

Nikolai Prochorov

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arXiv · 2410.01146

Finite and infinite degree Thurston maps with a small postsingular set

Nikolai Prochorov

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Abstract

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 Teichm\"uller space. This analysis also allows us to derive various properties of Hurwitz classes of the corresponding Thurston maps.

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BibTeX RIS

Nikolai Prochorov. 2024-10-02. Finite and infinite degree Thurston maps with a small postsingular set. https://arxiv.org/abs/2410.01146

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