{"title":"Rigidity and classification results for large-type Artin groups","authors":"Jingyin Huang, Damian Osajda, Nicolas Vaskou","doi":"arxiv-2407.19940","DOIUrl":null,"url":null,"abstract":"We compute the automorphism group of the intersection graph of many\nlarge-type Artin groups. This graph is an analogue of the curve graph of\nmapping class groups but in the context of Artin groups. As an application, we\ndeduce a number of rigidity and classification results for these groups,\nincluding computation of outer automorphism groups, commensurability\nclassification, quasi-isometric rigidity, measure equivalence rigidity, orbit\nequivalence rigidity, rigidity of lattice embedding, and rigidity of\ncross-product von Neumann algebra.","PeriodicalId":501114,"journal":{"name":"arXiv - MATH - Operator Algebras","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-07-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Operator Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2407.19940","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We compute the automorphism group of the intersection graph of many
large-type Artin groups. This graph is an analogue of the curve graph of
mapping class groups but in the context of Artin groups. As an application, we
deduce a number of rigidity and classification results for these groups,
including computation of outer automorphism groups, commensurability
classification, quasi-isometric rigidity, measure equivalence rigidity, orbit
equivalence rigidity, rigidity of lattice embedding, and rigidity of
cross-product von Neumann algebra.