{"title":"比尔曼-希尔登捆包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":49533,"journal":{"name":"Siberian Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"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\":49533,\"journal\":{\"name\":\"Siberian Mathematical Journal\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-02-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Siberian Mathematical Journal\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1134/s0037446624010117\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Siberian Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0037446624010117","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
期刊介绍：
Siberian Mathematical Journal is journal published in collaboration with the Sobolev Institute of Mathematics in Novosibirsk. The journal publishes the results of studies in various branches of mathematics.
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