${\mathrm{SL}}_2(\mathbb{R})$-dynamics on the moduli space of one-holed tori

Adrien Boulanger, Selim Ghazouani

We study the ${\mathrm{SL}}_2(\mathbb{R})$-action on the moduli space of (triangulable) dilation tori with one boundary component. We prove that every orbit is either closed or dense…