Relative systoles in hyperelliptic translation surfaces

Corentin Boissy (1) , Slavyana Geninska (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

In this paper we prove that the systole fonction on a connected component of area one translation surfaces admits a local maximum that is not a global maximum if and only if the connected component is not hyperelliptic.

Domaines: Topologie géométrique [math.GT]

Corentin Boissy, Slavyana Geninska. Relative systoles in hyperelliptic translation surfaces. 2020. ⟨hal-02909732⟩