{"title":"Birman–Hilden Bundles. I","authors":"A. V. Malyutin","doi":"10.1134/s0037446624010117","DOIUrl":null,"url":null,"abstract":"<p>A topological fibered space is a Birman–Hilden space\nwhenever in each isotopic pair of its fiber-preserving\n(taking each fiber to a fiber) self-homeomorphisms\nthe homeomorphisms are also fiber-isotopic\n(isotopic through fiber-preserving homeomorphisms).\nWe present a series of sufficient conditions\nfor a fiber bundle over the circle\nto be a Birman–Hilden space.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446624010117","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
A topological fibered space is a Birman–Hilden space
whenever in each isotopic pair of its fiber-preserving
(taking each fiber to a fiber) self-homeomorphisms
the homeomorphisms are also fiber-isotopic
(isotopic through fiber-preserving homeomorphisms).
We present a series of sufficient conditions
for a fiber bundle over the circle
to be a Birman–Hilden space.
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