2022/11/21 by Dragomir Šarić, Yilin Wang, Šarić, Dragomir +3
Mathematics · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Complex Variables (math.CV) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2211.11497
openalex publication_date 2022/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We introduce and the study the space of homeomorphisms of the circle (up to Möbius transformations) which are in ℓ2 with respect to modular coordinates called diamond shears along the edges of the Farey tessellation. Diamond shears are related combinatorially to shear coordinates, and are also closely related to the log Λ-lengths of decorated Teichmüller space introduced by Penner. We obtain sharp results comparing this new class to the Weil-Petersson class and Hölder classes of circle homeomorphisms. We also express the Weil-Petersson metric tensor and symplectic form in terms of infinitesimal shears and diamond shears.