辫状群 m$ 级同余子群的生成器

arXiv - MATH - Group Theory Pub Date : 2024-09-15 DOI:arxiv-2409.09612

Ishan Banerjee, Peter Huxford

{"title":"辫状群 m$ 级同余子群的生成器","authors":"Ishan Banerjee, Peter Huxford","doi":"arxiv-2409.09612","DOIUrl":null,"url":null,"abstract":"We prove for $m\\geq1$ and $n\\geq5$ that the level $m$ congruence subgroup\n$B_n[m]$ of the braid group $B_n$ associated to the integral Burau\nrepresentation $B_n\\to\\mathrm{GL}_n(\\mathbb{Z})$ is generated by $m$th powers\nof half-twists and the braid Torelli group. This solves a problem of Margalit,\ngeneralizing work of Assion, Brendle--Margalit, Nakamura, Stylianakis and\nWajnryb.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Generators for the level $m$ congruence subgroups of braid groups\",\"authors\":\"Ishan Banerjee, Peter Huxford\",\"doi\":\"arxiv-2409.09612\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove for $m\\\\geq1$ and $n\\\\geq5$ that the level $m$ congruence subgroup\\n$B_n[m]$ of the braid group $B_n$ associated to the integral Burau\\nrepresentation $B_n\\\\to\\\\mathrm{GL}_n(\\\\mathbb{Z})$ is generated by $m$th powers\\nof half-twists and the braid Torelli group. This solves a problem of Margalit,\\ngeneralizing work of Assion, Brendle--Margalit, Nakamura, Stylianakis and\\nWajnryb.\",\"PeriodicalId\":501037,\"journal\":{\"name\":\"arXiv - MATH - Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.09612\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.09612","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

对于 $m\geq1$ 和 $n\geq5$，我们证明辫子群 $B_n$ 的 $m$ 级全等子群 $B_n[m]$是由半捻子的 $m$ 次幂和辫子托雷利群生成的。这解决了Margalit的一个问题，推广了Assion、Brendle--Margalit、Nakamura、Stylianakis和Wajnryb的工作。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Generators for the level $m$ congruence subgroups of braid groups

We prove for $m\geq1$ and $n\geq5$ that the level $m$ congruence subgroup $B_n[m]$ of the braid group $B_n$ associated to the integral Burau representation $B_n\to\mathrm{GL}_n(\mathbb{Z})$ is generated by $m$th powers of half-twists and the braid Torelli group. This solves a problem of Margalit, generalizing work of Assion, Brendle--Margalit, Nakamura, Stylianakis and Wajnryb.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

arXiv - MATH - Group Theory

自引率

0.00%

发文量