{"title":"Holonomy of complex projective structures on surfaces with prescribed branch data","authors":"Thomas Le Fils","doi":"10.1112/topo.12287","DOIUrl":null,"url":null,"abstract":"<p>We characterize the representations of the fundamental group of a closed surface to <math>\n <semantics>\n <mrow>\n <msub>\n <mi>PSL</mi>\n <mn>2</mn>\n </msub>\n <mrow>\n <mo>(</mo>\n <mi>C</mi>\n <mo>)</mo>\n </mrow>\n </mrow>\n <annotation>$\\mathrm{PSL}_2(\\mathbb {C})$</annotation>\n </semantics></math> that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the holonomies of the spherical metrics with prescribed integral conical angles and the holonomies of affine structures with fixed conical angles on closed surfaces.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12287","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12287","RegionNum":2,"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 characterize the representations of the fundamental group of a closed surface to that arise as the holonomy of a branched complex projective structure with fixed branch divisor. In particular, we compute the holonomies of the spherical metrics with prescribed integral conical angles and the holonomies of affine structures with fixed conical angles on closed surfaces.
期刊介绍：
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.
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