亏格 $\geq 3$ 曲面的映射类群不虚满射到 $\mathbb{Z}$
几何拓扑
2020-12-03 v2 代数几何
动力系统
群论
摘要
我们证明了 Nikolai Ivanov 的一个著名猜想：若 是亏格 的曲面（具有任意数量的穿孔与边界分支）， 为 的映射类群， 为有限指数子群，则 不虚满射到 。作为推论，当 是 （带 个标记点的亏格 复代数曲线模空间）的有限覆盖时，有 。
引用
@article{arxiv.2008.10643,
title = {Mapping class groups of surfaces of genus $\geq 3$ do not virtually surject to $\mathbb{Z}$},
author = {Asaf Hadari},
journal= {arXiv preprint arXiv:2008.10643},
year = {2020}
}
备注
The central problem is that Lemmas 5.3 and 5.4 in the paper (the folding trick and the folding trick for covers) are incorrect. As these lemmas are the heart of the rest of the proof, I am withdrawing the claim. I would like to extend special thanks to Julien Marche, Bram Petri, and Maxime Wolff for their careful reading and comments that lead to the discovery of the problems in the proof