Affine Invariant Submanifolds with Completely Degenerate\n Kontsevich-Zorich Spectrum

2013/02/04 by David Aulicino, Aulicino, David
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1302.0913

openalex publication_date 2013/02/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28

Abstract

We prove that if the Lyapunov spectrum of the Kontsevich-Zorich cocycle over\nan affine SL(2,\ℝ)-invariant submanifold is completely degenerate,\ni.e. \λ₂ = \⋯ = \λ_g = 0, then the submanifold must be an\narithmetic Teichmueller curve in the moduli space of Abelian differentials over\nsurfaces of genus three, four, or five. As a corollary, we prove that there are\nat most finitely many such Teichmueller curves.\n

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