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arXiv · 2403.14923

Translation surfaces with large systoles

Peter Buser·Eran Makover·Bjoern Muetzel
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Abstract

In this paper we continue to investigate the systolic landscape of translation surfaces started in [CHMW]. We show that there is an infinite sequence of surfaces $(S_{g_k})_k$ of genus $g_k$, where $g_k \to \infty$ with large systoles. On the other hand we show that for hyperelliptic surfaces we can find a suitable homology basis, where a large number of loops that induce the basis are short.

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Peter Buser, Eran Makover, Bjoern Muetzel. 2024-03-22. Translation surfaces with large systoles. https://arxiv.org/abs/2403.14923

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