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The algebraic approach to Teichmüller spaces hints towards the more general consideration of representations of \(\pi _1(S_g)\) to Lie groups other than \(\mathrm {PSL}_2(\mathbb {R})\) . This leads naturally to the consideration of character varieties and the notion of higher-rank Teichmüller spaces, which are connected components of the character variety entirely consisting of discrete and faithful representations. Two main examples of these spaces are Hitchin components and maximal components studied in the following chapters.

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Higher-Rank Teichmüller Spaces

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  • 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

The algebraic approach to Teichmüller spaces hints towards the more general consideration of representations of \(\pi _1(S_g)\) to Lie groups other than \(\mathrm {PSL}_2(\mathbb {R})\) . This leads naturally to the consideration of character varieties and the notion of higher-rank Teichmüller spaces, which are connected components of the character variety entirely consisting of discrete and faithful representations. Two main examples of these spaces are Hitchin components and maximal components studied in the following chapters.