Hatcher-Thurston complex for surfaces with non-planar ends

Manvendra Somvanshi

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arXiv · 2602.22393

Hatcher-Thurston complex for surfaces with non-planar ends

Manvendra Somvanshi

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Abstract

In this paper, for each $k\in \mathbb{N}$, we define a complex $\Gamma_k(S)$ for an infinite-type surface $S$ with non-planar ends, which serves as an analog of the Hatcher-Thurston complex for the infinite-type setting. We show that $\Gamma_k(S)$ is connected, simply connected, and that the automorphism group of $\Gamma_k(S)$ is isomorphic to the extended mapping class group.

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Manvendra Somvanshi. 2026-02-25. Hatcher-Thurston complex for surfaces with non-planar ends. https://arxiv.org/abs/2602.22393

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