Parity of the spin structure defined by a quadratic differential

Lanneau, Erwan¹

¹ Institut de mathématiques de Luminy, Case 907, 163 Avenue de Luminy, F-13288 Marseille Cedex 9, France

Geometry & topology, Tome 8 (2004) no. 2, pp. 511-538.

Résumé

According to the work of Kontsevich–Zorich, the invariant that classifies non-hyperelliptic connected components of the moduli spaces of Abelian differentials with prescribed singularities, is the parity of the spin structure.

We show that for the moduli space of quadratic differentials, the spin structure is constant on every stratum where it is defined. In particular this disproves the conjecture that it classifies the non-hyperelliptic connected components of the strata of quadratic differentials with prescribed singularities. An explicit formula for the parity of the spin structure is given.

Détail

DOI : 10.2140/gt.2004.8.511

Keywords: quadratic differentials, Teichmüller geodesic flow, moduli space, measured foliations, spin structure

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