{"title":"表面束截面","authors":"J. Hillman","doi":"10.2140/gtm.2015.19.1","DOIUrl":null,"url":null,"abstract":"A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:\\pi_1(B)\\to{Out}(\\pi_1(F))$ factors through $Aut(\\pi_1(F))$ and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression $d^2_{2,0}$ in the homology LHS spectral sequence of a central extension is evaluation of the extension class. Examples with hyperbolic fibre and no section (based on ideas of Endo) added.","PeriodicalId":115248,"journal":{"name":"Geometry and Topology Monographs","volume":"02 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Sections of surface bundles\",\"authors\":\"J. Hillman\",\"doi\":\"10.2140/gtm.2015.19.1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:\\\\pi_1(B)\\\\to{Out}(\\\\pi_1(F))$ factors through $Aut(\\\\pi_1(F))$ and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression $d^2_{2,0}$ in the homology LHS spectral sequence of a central extension is evaluation of the extension class. Examples with hyperbolic fibre and no section (based on ideas of Endo) added.\",\"PeriodicalId\":115248,\"journal\":{\"name\":\"Geometry and Topology Monographs\",\"volume\":\"02 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2013-09-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Geometry and Topology Monographs\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.2140/gtm.2015.19.1\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Geometry and Topology Monographs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2140/gtm.2015.19.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A bundle with base $B$ and fibre $F$ aspherical closed surfaces has a section if and only if the action $:\pi_1(B)\to{Out}(\pi_1(F))$ factors through $Aut(\pi_1(F))$ and a cohomology class is 0. We simplify and make more explicit the latter condition. We also show that the transgression $d^2_{2,0}$ in the homology LHS spectral sequence of a central extension is evaluation of the extension class. Examples with hyperbolic fibre and no section (based on ideas of Endo) added.
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