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<p>We define Fenchel-Nielsen coordinates for representations of surface groups to <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10711_2025_1021_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="59" /> </InlineMediaObject> <EquationSource Format="TEX">\(\textrm{SL}(3,{\mathbb C})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mtext>SL</mtext> <mo stretchy="false">(</mo> <mn>3</mn> <mo>,</mo> <mi mathvariant="double-struck">C</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>. We also show how these coordinates relate to the classical Fenchel-Nielsen coordinates and to their generalisations by Kourouniotis, Tan, Goldman, Zhang and Parker-Platis.</p>

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Fenchel-Nielsen coordinates for \(\textrm{SL}(3,{\mathbb C})\) representations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月17日

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  • Rodrigo Dávila Figueroa,
  • John R. Parker

摘要

We define Fenchel-Nielsen coordinates for representations of surface groups to \(\textrm{SL}(3,{\mathbb C})\) SL ( 3 , C ) . We also show how these coordinates relate to the classical Fenchel-Nielsen coordinates and to their generalisations by Kourouniotis, Tan, Goldman, Zhang and Parker-Platis.