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Connected components of the G-character variety are distinguished by a primary topological invariant taking values in \(\pi _1(G)\) . For Hermitian Lie groups, this is the Toledo invariant, which is bounded in absolute value by a Milnor–Wood type inequality. In the case of Hermitian groups of tube type, the components where the Toledo invariant attains its maximal value are known as maximal components. These form another class of higher-rank Teichmüller spaces. In this chapter we discuss coordinate systems that allow their explicit study.

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Maximal Representations

  • 章节

  • 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

Connected components of the G-character variety are distinguished by a primary topological invariant taking values in \(\pi _1(G)\) . For Hermitian Lie groups, this is the Toledo invariant, which is bounded in absolute value by a Milnor–Wood type inequality. In the case of Hermitian groups of tube type, the components where the Toledo invariant attains its maximal value are known as maximal components. These form another class of higher-rank Teichmüller spaces. In this chapter we discuss coordinate systems that allow their explicit study.