{"title":"非定向面上辫状群的几何表示","authors":"Michał Stukow, Błażej Szepietowski","doi":"arxiv-2408.04707","DOIUrl":null,"url":null,"abstract":"We classify homomorphisms from the braid group on $n$ strands to the pure\nmapping class group of a nonoriantable surface of genus $g$. For $n\\ge 14$ and\n$g\\le 2\\lfloor{n/2}\\rfloor+1$ every such homomorphism is either cyclic, or it\nmaps standard generators of the braid group to either distinct Dehn twists, or\ndistinct crosscap transpositions, possibly multiplied by the same element of\nthe centralizer of the image.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"263 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Geometric representations of the braid group on a nonorientable surface\",\"authors\":\"Michał Stukow, Błażej Szepietowski\",\"doi\":\"arxiv-2408.04707\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We classify homomorphisms from the braid group on $n$ strands to the pure\\nmapping class group of a nonoriantable surface of genus $g$. For $n\\\\ge 14$ and\\n$g\\\\le 2\\\\lfloor{n/2}\\\\rfloor+1$ every such homomorphism is either cyclic, or it\\nmaps standard generators of the braid group to either distinct Dehn twists, or\\ndistinct crosscap transpositions, possibly multiplied by the same element of\\nthe centralizer of the image.\",\"PeriodicalId\":501271,\"journal\":{\"name\":\"arXiv - MATH - Geometric Topology\",\"volume\":\"263 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Geometric Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.04707\",\"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 - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.04707","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Geometric representations of the braid group on a nonorientable surface
We classify homomorphisms from the braid group on $n$ strands to the pure
mapping class group of a nonoriantable surface of genus $g$. For $n\ge 14$ and
$g\le 2\lfloor{n/2}\rfloor+1$ every such homomorphism is either cyclic, or it
maps standard generators of the braid group to either distinct Dehn twists, or
distinct crosscap transpositions, possibly multiplied by the same element of
the centralizer of the image.