Two remarks about multicurve graphs on infinite-type surfaces

Julio Aroca

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arXiv · 1803.05371

Two remarks about multicurve graphs on infinite-type surfaces

Julio Aroca

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Abstract

After Fossas-Parlier, we consider two graphs $\mathcal{G}_{0}(S)$ and $\mathcal{G}_{\infty}(S)$, constructed from multicurves on connected, orientable surfaces of infinite-type. Our first result asserts that $\mathcal{G}_{\infty}(S)$ has finite diameter, which extends a result of Fossas-Parlier. Next, we prove that the group of (label-preserving) automorphisms of $\mathcal{G}_{0}(S)$ is the extended mapping class group of $S$, which may be regarded as an infinite-type analog of a theorem of Margalit about pants complexes.

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Julio Aroca. 2018-03-14. Two remarks about multicurve graphs on infinite-type surfaces. https://arxiv.org/abs/1803.05371

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