Systolic geometry of translation surfaces

Tobias Columbus; Frank Herrlich; Bjoern Muetzel; Gabriela Weitze-Schmithüsen

doi:10.1080/10586458.2022.2108946

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arXiv · 1809.10327

Systolic geometry of translation surfaces

Tobias Columbus·Frank Herrlich·Bjoern Muetzel·Gabriela Weitze-Schmithüsen

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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 $\mathcal{H}(1,1)$. We compute the maximal systolic ratio of all origamis in $\mathcal{H}(1,1)$ with up to 67 squares. These computations support a conjecture of Judge and Parlier about the maximal systolic ratio in $\mathcal{H}(1,1)$.

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BibTeX RIS

Tobias Columbus, Frank Herrlich, Bjoern Muetzel, Gabriela Weitze-Schmithüsen. 2022-09-12. Systolic geometry of translation surfaces. https://doi.org/10.1080/10586458.2022.2108946

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