Reduction theory for mapping class groups and applications to moduli spaces

DOI10.1515/CRELLE.2010.086zbMath1213.30082arXiv0801.1589OpenAlexW2962928725MaRDI QIDQ3065806

Enrico Leuzinger

Publication date: 6 January 2011

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0801.1589

zbMATH Keywords

Teichmüller spacemapping class groupsemi-simple Lie grouparithmetic group

Mathematics Subject Classification ID

Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10) Teichmüller theory for Riemann surfaces (30F60) Lie groups (22E99) Curves in algebraic geometry (14H99)

Related Items (6)

The asymptotic Schottky problem ⋮ A Gauss-Bonnet formula for moduli spaces of Riemann surfaces ⋮ Curve Complexes Versus Tits Buildings: Structures and Applications ⋮ Almost-isometry between the Teichmüller metric and the arc-length-spectrum metric on moduli space for surfaces with boundary ⋮ Metric distortion in the geometric Schottky problem ⋮ Almost-isometry between the Teichmüller metric and the length-spectrum metric on reduced moduli space for surfaces with boundary

Cites Work

• Tilings and finite energy retractions of locally symmetric spaces
• Rank-1 phenomena for mapping class groups
• On polyhedral retracts and compactifications of locally symmetric spaces
• Extremal length estimates and product regions in Teichmüller space
• The moduli space of Riemann surfaces is Kähler hyperbolic
• Dimension and rank for mapping class groups
• Complexes of curves and the Teichmüller modular group
• A rough fundamental domain for Teichmüller spaces

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