English

Systoles in translation surfaces

Metric Geometry 2022-03-30 v3 Geometric Topology

Abstract

For a translation surface, we define the systole to be the length of the shortest saddle connection. We give a characterization of the maxima of the systole function on a stratum, and give a family of examples providing local but nonglobal maxima on each stratum of genus at least three. We further study the relation between (locally) maximal values of the systole function and the number of shortest saddle connections.

Cite

@article{arxiv.1707.05060,
  title  = {Systoles in translation surfaces},
  author = {Corentin Boissy and Slavyana Geninska},
  journal= {arXiv preprint arXiv:1707.05060},
  year   = {2022}
}

Comments

Journal ref: Bull SMF 149 (2021)

R2 v1 2026-06-22T20:48:44.110Z