有限不变指标为 1 的曲面曲线图
几何拓扑
2021-09-16 v2 群论
摘要
在本注记中，我们朝 Durham--Fanoni--Vlamis 的一个猜想取得进展，证明了每个有限不变指标为 1 且无不可位移紧子曲面的无限型曲面都不具有好的曲线图，即一种连通图，其顶点表示本质简单闭曲线的同伦类，且自然的映射类群作用具有无穷直径轨道。我们的论证使用了 Mann--Rafi 在研究大映射类群粗几何时所发展的工具。
引用
@article{arxiv.2106.14916,
title = {Curve graphs of surfaces with finite-invariance index 1},
author = {Justin Lanier and Marissa Loving},
journal= {arXiv preprint arXiv:2106.14916},
year = {2021}
}
备注
8 pages. A hypothesis has been added to the main theorem to accommodate an error in the proof of Lemma 3.2 in the previous version. The proofs of Propositions 4.3 and 4.4 in the previous version have been combined into the proof of Proposition 4.4. A new Proposition 4.3 has been added to address a gap in the proof of Proposition 4.4; its proof relies on work of Malestein--Tao