具有有限不变指标曲面的曲线图 \(1\)

Pub Date : 2022-06-28 DOI:10.3336/gm.57.1.08

Justin Lanier, Marissa Loving

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引用次数: 2

摘要

在这篇文章中，我们对Durham-Fanoni-Vlamis的一个猜想取得了进展，证明了每一个具有fi - ni -t -invariance指标\(1\)且没有不可置换紧致子曲面的无限型曲面都不可能有一个好的曲线图，即顶点表示本质简单闭曲线的同伦类且具有具有无限直径轨道的自然映射类群作用的连通图。我们的论证使用了Mann-Rafi在研究大映射类群的粗糙几何时开发的工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Graphs of curves for surfaces with finite-invariance index \(1\)

In this note we make progress toward a conjecture of Durham–Fanoni–Vlamis, showing that every infinite-type surface with finite-invariance index \(1\) and no nondisplaceable compact subsurfaces fails to have a good graph of curves, that is, a connected graph where vertices represent homotopy classes of essential simple closed curves and with a natural mapping class group action having infinite diameter orbits. Our arguments use tools developed by Mann–Rafi in their study of the coarse geometry of big mapping class groups.

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