Configurations of saddle connections of quadratic differentials on CP1 and on hyperelliptic Riemann surfaces
Abstract
Configurations of rigid collections of saddle connections are invariants of connected components of strata of the moduli space of quadratic differentials. They have been classified for strata of Abelian differentials by Eskin, Masur and Zorich. Similar work for strata of quadratic differentials has been done by Masur and Zorich, although in that case the connected components where not distinguished. We classify the configurations for quadratic differentials on $\mathbb{CP}^1$ and on hyperelliptic connected components of the moduli space of quadratic differentials. We show, in particular, that, when the genus is greater than 5, any configuration that appears in the hyperelliptic connected component of a stratum also appears in the nonhyperelliptic one.
Domains
Geometric Topology [math.GT]
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