{"title":"Leighton’s theorem and regular cube complexes","authors":"Daniel J. Woodhouse","doi":"10.2140/agt.2023.23.3395","DOIUrl":null,"url":null,"abstract":"Leighton's graph covering theorem states that two finite graphs with common universal cover have a common finite cover. We generalize this to a large family of non-positively curved special cube complexes that form a natural generalization of regular graphs. This family includes both hyperbolic and non-hyperbolic CAT(0) cube complexes.","PeriodicalId":50826,"journal":{"name":"Algebraic and Geometric Topology","volume":"2 1","pages":"0"},"PeriodicalIF":0.6000,"publicationDate":"2023-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebraic and Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/agt.2023.23.3395","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Leighton's graph covering theorem states that two finite graphs with common universal cover have a common finite cover. We generalize this to a large family of non-positively curved special cube complexes that form a natural generalization of regular graphs. This family includes both hyperbolic and non-hyperbolic CAT(0) cube complexes.
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