当前位置: X-MOL 学术Math. Res. Lett. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
The Birman exact sequence does not virtually split
Mathematical Research Letters ( IF 1 ) Pub Date : 2021-05-13 , DOI: 10.4310/mrl.2021.v28.n2.a3
Lei Chen 1 , Nick Salter 2
Affiliation  

This paper answers a basic question about the Birman exact sequence in the theory of mapping class groups. We prove that the Birman exact sequence does not admit a section over any subgroup $\Gamma$ contained in the Torelli group with finite index. A fortiori this implies that there is no multi-section for the universal surface bundle with Torelli monodromy. This theorem was announced in a 1990 preprint of G. Mess, but an error was uncovered and described in a recent paper of the first author.

中文翻译:

Birman的确切顺序几乎没有分裂

本文回答了有关映射类组理论中Birman精确序列的一个基本问题。我们证明Birman精确序列不允许在具有有限索引的Torelli组中包含的任何子组$ \ Gamma $上截取截面。更不用说这意味着不存在多部用于与单值托雷利通用表面束。该定理在1990年的G. Mess的预印本中宣布,但在第一作者的最新论文中发现并描述了一个错误。
更新日期:2021-05-14
down
wechat
bug