{"title":"Birman–Hilden Bundles. II","authors":"A. V. Malyutin","doi":"10.1134/s0037446624020101","DOIUrl":null,"url":null,"abstract":"<p>We study the structure of self-homeomorphism groups of fibered manifolds.\nA fibered topological space\nis a Birman–Hilden space\nwhenever in each isotopic pair of its fiber-preserving\n(taking each fiber to a fiber)\nself-homeomorphisms\nthe homeomorphisms are also fiber-isotopic\n(isotopic through fiber-preserving homeomorphisms).\nWe prove in particular that\nthe Birman–Hilden class contains\nall compact connected locally trivial surface bundles over the circle,\nincluding nonorientable ones and those with nonempty boundary,\nas well as all closed orientable Haken 3-manifold bundles over the circle,\nincluding nonorientable ones.</p>","PeriodicalId":49533,"journal":{"name":"Siberian Mathematical Journal","volume":"31 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-03-25","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/s0037446624020101","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
We study the structure of self-homeomorphism groups of fibered manifolds.
A fibered topological 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 prove in particular that
the Birman–Hilden class contains
all compact connected locally trivial surface bundles over the circle,
including nonorientable ones and those with nonempty boundary,
as well as all closed orientable Haken 3-manifold bundles over the circle,
including nonorientable ones.
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.