Isomorphisms between curve graphs of infinite-type surfaces are geometric

Jesús Hernández Hernández; Israel Morales; Ferrán Valdez

Isomorphisms between curve graphs of infinite-type surfaces are geometric

Geometric Topology 2017-06-13 v1

Authors: Jesús Hernández Hernández , Israel Morales , Ferrán Valdez

Abstract

Let $\phi:\mathcal{C}(S)\to\mathcal{C}(S')$ be a simplicial isomorphism between the curve graphs of two infinite-type surfaces. In this paper we show that in this situation $S$ and $S'$ are homeomorphic and $\phi$ is induced by a homeomorphism $h:S\to S'$ .

Keywords

curve graphs infinite-type surfaces simplicial isomorphism geometric isomorphism homeomorphism

Cite

@article{arxiv.1706.03697,
  title  = {Isomorphisms between curve graphs of infinite-type surfaces are geometric},
  author = {Jesús Hernández Hernández and Israel Morales and Ferrán Valdez},
  journal= {arXiv preprint arXiv:1706.03697},
  year   = {2017}
}

Comments

12 pages, 5 figures

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