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The Teichmüller space can be coordinatized via the Fenchel–Nielsen length and twist parameters associated with a pants decomposition. For ciliated surfaces, one can alternatively use Thurston’s shear coordinates, whose transformation rules are particularly well-structured and naturally lead to cluster algebra structures.

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Coordinates on Teichmüller Space

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  • 出版模式：

    开放获取

  • 发表日期：

    2026年

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

摘要

The Teichmüller space can be coordinatized via the Fenchel–Nielsen length and twist parameters associated with a pants decomposition. For ciliated surfaces, one can alternatively use Thurston’s shear coordinates, whose transformation rules are particularly well-structured and naturally lead to cluster algebra structures.