Keywords

• Riemann surface
• translation surface
• meromorphic differential
• Loch Ness monster

Abstract On a Riemann surface $X$, every meromorphic abelian differential determines a translation surface and a representation $\chi:\pi_1(X)\to\mathbb{ℂ}$ called period character. In this seminar we shall talk about strata of meromorphic differential with prescribed zeros and poles. Strata admit a natural foliation in which every leaf comprises translation surfaces with the same period character. In the special case of $H(1,1;−2)$ each leaf is homeomorphic to the Loch Ness monster and it carries itself a transition structure.