Systolic geometry of translation surfaces
T Columbus, F Herrlich, B Muetzel… - Experimental …, 2024 - Taylor & Francis
T Columbus, F Herrlich, B Muetzel, G Weitze-Schmithüsen
Experimental Mathematics, 2024•Taylor & FrancisIn this paper we investigate the systolic landscape of translation surfaces for fixed genus and
fixed angles of their cone points. We furthermore study how the systoles of a translation
surface relate to the systoles of its graph of saddle connections. This allows us to develop an
algorithm to compute the systolic ratio of origamis in the stratum H (1, 1). We compute the
maximal systolic ratio of all origamis in H (1, 1) with up to 67 squares. These computations
support a conjecture of Judge and Parlier about the maximal systolic ratio in H (1, 1).
fixed angles of their cone points. We furthermore study how the systoles of a translation
surface relate to the systoles of its graph of saddle connections. This allows us to develop an
algorithm to compute the systolic ratio of origamis in the stratum H (1, 1). We compute the
maximal systolic ratio of all origamis in H (1, 1) with up to 67 squares. These computations
support a conjecture of Judge and Parlier about the maximal systolic ratio in H (1, 1).
Abstract
In this paper we investigate the systolic landscape of translation surfaces for fixed genus and fixed angles of their cone points. We furthermore study how the systoles of a translation surface relate to the systoles of its graph of saddle connections. This allows us to develop an algorithm to compute the systolic ratio of origamis in the stratum . We compute the maximal systolic ratio of all origamis in with up to 67 squares. These computations support a conjecture of Judge and Parlier about the maximal systolic ratio in .
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