Configurations of saddle connections of quadratic differentials on CP1 and on hyperelliptic Riemann surfaces

Details Configurations of saddle connections of quadratic differentials on CP1 and on hyperelliptic Riemann surfaces Configurations of saddle connections of quadratic differentials on CP1 and on hyperelliptic Riemann surfaces

2007-05-22

arxiv.org/abs/0705.3142v2

Mathematics

Geometric Topology

34 pages, 12 figures, submitted, improved presentation and typography

Scientific paper

Configurations of rigid collections of saddle connections are connected component invariants for 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 in Masur and Zorich, although in that case the connected components were not distinguished. We classify the configurations for quadratic differentials on the Riemann sphere and on hyperelliptic connected components of the moduli space of quadratic differentials. We show that, in genera greater than five, any configuration that appears in the hyperelliptic connected component of a stratum also appears in the non-hyperelliptic one.

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