Translation surfaces with large systoles

2024/03/22 by Peter Buser, Buser, Peter, Eran Makover +3
Materials Science · #30F10 #32G15 and 53C22 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Synthesis and properties of polymers

paper · pdf · doi:10.48550/arxiv.2403.14923

openalex publication_date 2024/03/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_gk)_k of genus g_k, where g_k → ∞ 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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