Translation surfaces with large systoles

Peter Buser; Eran Makover; Bjoern Muetzel

Translation surfaces with large systoles

Differential Geometry 2024-03-25 v1 Complex Variables Metric Geometry

Authors: Peter Buser , Eran Makover , Bjoern Muetzel

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.

Keywords

surface theory

Cite

@article{arxiv.2403.14923,
  title  = {Translation surfaces with large systoles},
  author = {Peter Buser and Eran Makover and Bjoern Muetzel},
  journal= {arXiv preprint arXiv:2403.14923},
  year   = {2024}
}

Comments

15 pages, 7 figures

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