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Spectral networks appear in the theory of linear differential equations on Riemann surfaces. A special approach to solve these differential equations is the WKB method giving formal solutions. Using Borel resummation, these formal solutions can be converted into exact solutions on the complement of a graph—the spectral network. We explore this approach and link it to the abelianization process. We will mainly stick to the case of \(\mathrm {SL}_2(\mathbb {C})\) .

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WKB Method and Stokes Graphs

  • 章节

  • 出版模式：

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  • 发表日期：

    2026年

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  • Clarence Kineider,
  • Georgios Kydonakis,
  • Eugen Rogozinnikov,
  • Valdo Tatitscheff,
  • Alexander Thomas

摘要

Spectral networks appear in the theory of linear differential equations on Riemann surfaces. A special approach to solve these differential equations is the WKB method giving formal solutions. Using Borel resummation, these formal solutions can be converted into exact solutions on the complement of a graph—the spectral network. We explore this approach and link it to the abelianization process. We will mainly stick to the case of \(\mathrm {SL}_2(\mathbb {C})\) .