Generalizations of the Eierlegende-Wollmilchsau

2020/11/18 by Paul Apisa, Apisa, Paul, Alex Wright +1 · 2 citations
Mathematics · #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.2011.09452

openalex publication_date 2020/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify a natural collection of GL(2,R)-invariant subvarieties, which includes loci of double covers, the orbits of the Eierlegende-Wollmilchsau, Ornithorynque, and Matheus-Yoccoz surfaces, and loci appearing naturally in the study of the complex geometry of Teichmuller space. This classification is the key input in subsequent work of the authors that classifies "high rank" invariant subvarieties, and in subsequent work of the first author that classifies certain invariant subvarieties with "Lyapunov spectrum as degenerate as possible". We also derive applications to the complex geometry of Teichmuller space and construct new examples, which negatively resolve two questions of Mirzakhani and Wright and illustrate previously unobserved phenomena for the finite blocking problem.

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