Hatcher-Thurston complex for surfaces with non-planar ends

Manvendra Somvanshi

Hatcher-Thurston complex for surfaces with non-planar ends

Geometric Topology 2026-02-27 v1

Authors: Manvendra Somvanshi

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.

Keywords

mapping class groups mapping class groups of surfaces group theory

Cite

@article{arxiv.2602.22393,
  title  = {Hatcher-Thurston complex for surfaces with non-planar ends},
  author = {Manvendra Somvanshi},
  journal= {arXiv preprint arXiv:2602.22393},
  year   = {2026}
}

Comments

15 pages, 11 figures

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