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<p>We prove the representation given by a stable <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3249_Article_IEq3.gif" Format="GIF" Height="12" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\(\alpha _1\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>α</mi> <mn>1</mn> </msub> </math></EquationSource> </InlineEquation>-cyclic parabolic <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3249_Article_IEq4.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="65" /> </InlineMediaObject> <EquationSource Format="TEX">\({\textrm{SO}}_0(2,3)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>SO</mtext> <mn>0</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation>-Higgs bundle satisfying specific assumptions through the non-Abelian Hodge correspondence is <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="208_2025_3249_Article_IEq5.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="40" /> </InlineMediaObject> <EquationSource Format="TEX">\(\{\alpha _2\}\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <msub> <mi>α</mi> <mn>2</mn> </msub> <mo stretchy="false">}</mo> </mrow> </math></EquationSource> </InlineEquation>-almost dominated. This is a generalization of Filip’s result on weight 3 variation of Hodge structures and answers a question asked by Collier, Tholozan and Toulisse.</p>

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Non-maximal Anosov representations from surface groups to \(\textrm{SO}_0(2,3)\)

  • 期刊论文

  • 发表日期：

    2025年8月23日

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  • Junming Zhang

摘要

We prove the representation given by a stable \(\alpha _1\) α 1 -cyclic parabolic \({\textrm{SO}}_0(2,3)\) SO 0 ( 2 , 3 ) -Higgs bundle satisfying specific assumptions through the non-Abelian Hodge correspondence is \(\{\alpha _2\}\) { α 2 } -almost dominated. This is a generalization of Filip’s result on weight 3 variation of Hodge structures and answers a question asked by Collier, Tholozan and Toulisse.