Geometry & Topology, Vol. 8 (2004)
Paper no. 12, pages 511--538.
Parity of the spin structure defined by a quadratic differential
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.
Quadratic differentials, Teichmueller geodesic flow, moduli space, measured foliations, spin structure
AMS subject classification.
Primary: 32G15, 30F30, 30F60.
Secondary: 58F12, 57R15.
Submitted to GT on 29 July 2003.
(Revised 12 March 2004.)
Paper accepted 16 December 2004.
Paper published 13 March 2004.
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