{"title":"Classification of generalized Seifert fiber spaces","authors":"Fernando Galaz-Garcia, Jesús Núñez-Zimbrón","doi":"arxiv-2409.02216","DOIUrl":null,"url":null,"abstract":"We provide a symbolic classification of generalized Seifert fiber spaces,\nwhich were introduced by Mitsuishi and Yamaguchi in the classification of\ncollapsing Alexandrov $3$-spaces. Additionally, we show that the canonical\ndouble branched cover of a non-manifold generalized Seifert fiber space is a\nSeifert manifold and compute its symbolic invariants in terms of those of the\noriginal space.","PeriodicalId":501444,"journal":{"name":"arXiv - MATH - Metric Geometry","volume":"15 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Metric Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.02216","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 provide a symbolic classification of generalized Seifert fiber spaces,
which were introduced by Mitsuishi and Yamaguchi in the classification of
collapsing Alexandrov $3$-spaces. Additionally, we show that the canonical
double branched cover of a non-manifold generalized Seifert fiber space is a
Seifert manifold and compute its symbolic invariants in terms of those of the
original space.
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