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The Teichmüller space of a smooth surface S is the space of hyperbolic metrics on S, modulo diffeomorphisms isotopic to the identity. Equivalently, it parameterizes conformal (or complex) structures on S under the same equivalence. Via the holonomy representation, Teichmüller space can also be identified with a connected component of the \(\mathrm {PSL}_2(\mathbb {R})\) character variety. In this chapter, we set the main definitions and exhibit the holonomy representation explicitly.

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The Teichmüller Space

  • 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

The Teichmüller space of a smooth surface S is the space of hyperbolic metrics on S, modulo diffeomorphisms isotopic to the identity. Equivalently, it parameterizes conformal (or complex) structures on S under the same equivalence. Via the holonomy representation, Teichmüller space can also be identified with a connected component of the \(\mathrm {PSL}_2(\mathbb {R})\) character variety. In this chapter, we set the main definitions and exhibit the holonomy representation explicitly.