{"title":"椭圆型纤颤的分岔编织单态","authors":"Michael Lönne","doi":"10.1016/j.top.2006.03.001","DOIUrl":null,"url":null,"abstract":"<div><p>We propose to study a new kind of monodromy homomorphism for families of regular elliptic fibrations of a given differentiable fibration type to get a hold on topological properties of moduli stacks of elliptic surfaces.</p><p>In specific cases, including the most significant one, when all singular fibres are nodal irreducible rational curves, we compute the corresponding monodromy group, a subgroup of the mapping class group of the fibration base punctured at the singular values of the fibration.</p><p>We study a tentative algebraic characterisation and give implications for the group of diffeomorphisms compatible with the fibration.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"45 4","pages":"Pages 785-806"},"PeriodicalIF":0.0000,"publicationDate":"2006-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2006.03.001","citationCount":"2","resultStr":"{\"title\":\"On bifurcation braid monodromy of elliptic fibrations\",\"authors\":\"Michael Lönne\",\"doi\":\"10.1016/j.top.2006.03.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We propose to study a new kind of monodromy homomorphism for families of regular elliptic fibrations of a given differentiable fibration type to get a hold on topological properties of moduli stacks of elliptic surfaces.</p><p>In specific cases, including the most significant one, when all singular fibres are nodal irreducible rational curves, we compute the corresponding monodromy group, a subgroup of the mapping class group of the fibration base punctured at the singular values of the fibration.</p><p>We study a tentative algebraic characterisation and give implications for the group of diffeomorphisms compatible with the fibration.</p></div>\",\"PeriodicalId\":54424,\"journal\":{\"name\":\"Topology\",\"volume\":\"45 4\",\"pages\":\"Pages 785-806\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-07-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.top.2006.03.001\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Topology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0040938306000115\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938306000115","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On bifurcation braid monodromy of elliptic fibrations
We propose to study a new kind of monodromy homomorphism for families of regular elliptic fibrations of a given differentiable fibration type to get a hold on topological properties of moduli stacks of elliptic surfaces.
In specific cases, including the most significant one, when all singular fibres are nodal irreducible rational curves, we compute the corresponding monodromy group, a subgroup of the mapping class group of the fibration base punctured at the singular values of the fibration.
We study a tentative algebraic characterisation and give implications for the group of diffeomorphisms compatible with the fibration.
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