带标架映射类群与阿贝尔微分层的单值
几何拓扑
2020-05-14 v3 群论
摘要
本文借助拓扑单值表示研究了阿贝尔微分层与各类映射类群之间的关系。基于作者先前的工作，我们证明了一个微层的根本群满射到映射类群中保持底层黎曼曲面固定标架的子群上，从而给出单值群的完整刻画。在证明过程中，我们还表明这些“带标架映射类群”是有限生成的（尽管其指数为无穷），并给出了显式生成集。
引用
@article{arxiv.2002.02472,
title = {Framed mapping class groups and the monodromy of strata of Abelian differentials},
author = {Aaron Calderon and Nick Salter},
journal= {arXiv preprint arXiv:2002.02472},
year = {2020}
}
备注
New in version 3:we now treat all isotopy classes of framings in genus at least 5; previously we considered only the restricted class of framings of "holomorphic type". We have also given a further strengthening to the main result on framed mapping class groups, allowing a vastly broader class of generating sets