Steven B. Bradlow , Oscar García-Prada , Peter B. Gothen
{"title":"Homotopy groups of moduli spaces of representations","authors":"Steven B. Bradlow , Oscar García-Prada , Peter B. Gothen","doi":"10.1016/j.top.2007.06.001","DOIUrl":null,"url":null,"abstract":"<div><p>We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups <span><math><mstyle><mi>GL</mi></mstyle><mrow><mo>(</mo><mi>n</mi><mo>,</mo><mi>C</mi><mo>)</mo></mrow></math></span> and <span><math><mstyle><mi>U</mi></mstyle><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></mrow></math></span>. Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott–Morse theory on the corresponding moduli spaces.</p></div>","PeriodicalId":54424,"journal":{"name":"Topology","volume":"47 4","pages":"Pages 203-224"},"PeriodicalIF":0.0000,"publicationDate":"2008-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.top.2007.06.001","citationCount":"43","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Topology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0040938307000602","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 43
Abstract
We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups and . Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott–Morse theory on the corresponding moduli spaces.