Edge Preserving Maps of the Curve Graphs in Low Genus

Elmas Irmak

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arXiv · 1803.08806

Edge Preserving Maps of the Curve Graphs in Low Genus

Elmas Irmak

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Abstract

Let $R$ be a compact, connected, orientable surface of genus $g$ with $n$ boundary components. Let $\mathcal{C}(R)$ be the curve graph of $R$. We prove that if $g=0, n \geq 5$ or $g=1, n \geq 3$, and $λ: \mathcal{C}(R) \rightarrow\mathcal{C}(R)$ is an edge preserving map, then $λ$ is induced by a homeomorphism of $R$, and this homeomorphism is unique up to isotopy.

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BibTeX RIS

Elmas Irmak. 2018-03-21. Edge Preserving Maps of the Curve Graphs in Low Genus. https://arxiv.org/abs/1803.08806

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