Quasisymmetric maps, shears, lambda lengths and flips

DOI10.1007/s00209-024-03442-7arXiv2208.00494WikidataQ128168689 ScholiaQ128168689MaRDI QIDQ6120411

Dragomir Šarić, Hugo Parlier

Publication date: 20 February 2024

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2208.00494

zbMATH Keywords

hyperbolic planeshear coordinatesquasisymmetric maps

Mathematics Subject Classification ID

General low-dimensional topology (57M99) Moduli of Riemann surfaces, Teichmüller theory (complex-analytic aspects in several variables) (32G15) Teichmüller theory for Riemann surfaces (30F60)

Cites Work

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• Circle homeomorphisms and shears
• The decorated Teichmüller space of punctured surfaces
• Simultaneous flips on triangulated surfaces
• Sketch of a program for automorphic functions from universal Teichmüller theory to capture monstrous moonshine
• Thompson's group \(\mathcal T\) is the orientation-preserving automorphism group of a cellular complex
• Universal constructions in Teichmüller theory
• A presentation for the baseleaf preserving mapping class group of the punctured solenoid
• Teichmüller theory of the punctured solenoid
• Flip graphs for infinite type surfaces
• Shears for quasisymmetric maps
• Ideally, all infinite‐type surfaces can be triangulated

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