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Translation surfaces with large systoles (2403.14923v1)
Published 22 Mar 2024 in math.DG, math.CV, and math.MG
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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