2020/09/03 by Julien Boulanger, Boulanger, Julien
Mathematics · #51H99 #Algebraic Geometry and Number Theory #Algebraic geometry #Combinatorics #Connection (principal bundle) #Dynamical Systems (math.DS) #Element (criminal law) #FOS: Mathematics #Field (mathematics) #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometry #Group (periodic table) #Holonomy #Hyperbolic geometry #Mathematical Dynamics and Fractals #Mathematics #Physics #Pure mathematics #Quantum mechanics #Surface (topology) #Translation (biology)
paper · pdf · doi:10.48550/arxiv.2009.01748
openalex publication_date 2020/09/03 · openalex created_date 2023/10/04 · openalex updated_date 2026/07/28
We consider flow directions on the translation surfaces formed from double (2n+1)-gons, and give a sufficient condition in terms of a natural gcd algorithm for a direction to be hyperbolic in the sense that it is the fixed direction for some hyperbolic element of the Veech group of the surface. In particular, we give explicit points in the holonomy field of the double heptagon translation surface which are not so-called connection points. Among these are the central points of the heptagons, giving a negative answer to a question by P.Hubert and T.Schmidt.