{"title":"The Hrushovski property for compact special cube complexes","authors":"Brahim Abdenbi, Daniel T. Wise","doi":"10.1112/jlms.12907","DOIUrl":null,"url":null,"abstract":"<p>We show that any compact nonpositively curved cube complex <span></span><math>\n <semantics>\n <mi>Y</mi>\n <annotation>$Y$</annotation>\n </semantics></math> embeds in a compact nonpositively curved cube complex <span></span><math>\n <semantics>\n <mi>R</mi>\n <annotation>$R$</annotation>\n </semantics></math> where each combinatorial injective partial local isometry of <span></span><math>\n <semantics>\n <mi>Y</mi>\n <annotation>$Y$</annotation>\n </semantics></math> extends to an automorphism of <span></span><math>\n <semantics>\n <mi>R</mi>\n <annotation>$R$</annotation>\n </semantics></math>. When <span></span><math>\n <semantics>\n <mi>Y</mi>\n <annotation>$Y$</annotation>\n </semantics></math> is special and the collection of injective partial local isometries satisfies certain conditions, we show that <span></span><math>\n <semantics>\n <mi>R</mi>\n <annotation>$R$</annotation>\n </semantics></math> can be chosen to be special and the embedding <span></span><math>\n <semantics>\n <mrow>\n <mi>Y</mi>\n <mo>↪</mo>\n <mi>R</mi>\n </mrow>\n <annotation>$Y\\hookrightarrow R$</annotation>\n </semantics></math> can be chosen to be a local isometry.</p>","PeriodicalId":49989,"journal":{"name":"Journal of the London Mathematical Society-Second Series","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/jlms.12907","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the London Mathematical Society-Second Series","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/jlms.12907","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We show that any compact nonpositively curved cube complex embeds in a compact nonpositively curved cube complex where each combinatorial injective partial local isometry of extends to an automorphism of . When is special and the collection of injective partial local isometries satisfies certain conditions, we show that can be chosen to be special and the embedding can be chosen to be a local isometry.
我们证明,任何紧凑的非正曲立方体复数 Y $Y$ 都嵌入紧凑的非正曲立方体复数 R $R$ 中,其中 Y $Y$ 的每个组合注入局部等轴性都扩展为 R $R$ 的一个自变量。当 Y $Y$ 特殊且注入局部等距集合满足某些条件时,我们证明 R $R$ 可以被选择为特殊,并且嵌入 Y R $Y\hookrightarrow R$ 可以被选择为局部等距。
期刊介绍:
The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.