Moduli space of meromorphic differentials with marked horizontal separatrices

Corentin Boissy (1, 2)

1 AMU - Aix Marseille Université
2 I2M - Institut de Mathématiques de Marseille

We study framed translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces, for which a horizontal separatrix is marked for each pole or zero. Such geometric structures naturally appear when studying flat geometry surfaces " near " the Deligne-Mumford boundary. We provide an explicit formula for the number of connected components of the corresponding strata, and give a simple topological invariant that distinghish them.

Domains: Geometric Topology [math.GT]

Corentin Boissy. Moduli space of meromorphic differentials with marked horizontal separatrices. 2015. ⟨hal-01170878v2⟩