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<p>Let <i>G</i> be a complex reductive group and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(D\, \subset \, X\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>D</mi> <mspace width="0.166667em" /> <mo>⊂</mo> <mspace width="0.166667em" /> <mi>X</mi> </mrow> </math></EquationSource> </InlineEquation> a finite subset of a compact Riemann surface <i>X</i>. It was shown in Biswas and Jeffrey (Ann Math Québec 45: 213–219, 2021) that the moduli space of <i>G</i>–characters of <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\pi _1(X{\setminus } D)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mi>π</mi> <mn>1</mn> </msub> <mrow> <mo stretchy="false">(</mo> <mi>X</mi> <mo lspace="0.15em" rspace="0.15em" stretchy="false">\</mo> <mi>D</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> has a natural Poisson structure. We show that the moduli space of logarithmic <i>G</i>–connections on <i>X</i> singular over <i>D</i> has a Poisson structure. It is proved that the monodromy map from the moduli space of logarithmic <i>G</i>–connections to the moduli space of <i>G</i>–characters is Poisson structure preserving.</p>

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Poisson structure on character varieties, II

  • 期刊论文

  • 发表日期：

    2025年9月26日

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  • Indranil Biswas,
  • Lisa C. Jeffrey

摘要

Let G be a complex reductive group and \(D\, \subset \, X\) D ⊂ X a finite subset of a compact Riemann surface X. It was shown in Biswas and Jeffrey (Ann Math Québec 45: 213–219, 2021) that the moduli space of G–characters of \(\pi _1(X{\setminus } D)\) π 1 ( X \ D ) has a natural Poisson structure. We show that the moduli space of logarithmic G–connections on X singular over D has a Poisson structure. It is proved that the monodromy map from the moduli space of logarithmic G–connections to the moduli space of G–characters is Poisson structure preserving.