Systoles in translation surfaces

Corentin Boissy (1) , Slavyana Geninska (1)

1 IMT - Institut de Mathématiques de Toulouse UMR5219

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.

Mots clés: translation surfaces; systoles; moduli spaces

Domaines: Géométrie métrique [math.MG]; Topologie géométrique [math.GT]

Corentin Boissy, Slavyana Geninska. Systoles in translation surfaces. Bulletin de la société mathématique de France, 2021, 149 (2), pp.417-438. ⟨hal-01562013v3⟩