poster: On the connectivity of fibers of an isoperiodic foliation on a torus
speaker: Elizaveta Arzhakova (Leiden University)abstract: In 2016, B. Deroin, G. Calsamiglia, and S. Francaviglia (1 A transfer principle: from periods to isoperiodic foliations) showed that the fibers of an isoperiodic foliation of Abelian differentials are connected. However, the same problem remains open for the meromorphic differentials. In this poster I present my join project with B. Deroin and G. Calsamiglia on the connectivity of the isoperiodic leaves of meromorphic differentials in the case of a torus (two zeroes and two poles). We separately treat two cases: when the periods are complex, and when the periods are real. In the complex case a technique similar to 1 helps to obtain that the leaves are connected; in the case of real periods the volume argument fails, so we use algebraic methods to obtain the same result.
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