Volume 8, issue 2 (2004)

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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Parity of the spin structure defined by a quadratic differential

Erwan Lanneau

Geometry & Topology 8 (2004) 511–538

arXiv: math.GT/0210116

Abstract

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.

Keywords
quadratic differentials, Teichmüller geodesic flow, moduli space, measured foliations, spin structure
Mathematical Subject Classification 2000
Primary: 32G15
Secondary: 30F30, 30F60, 58F18
References
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Publication
Received: 29 July 2003
Revised: 12 March 2004
Accepted: 16 December 2004
Published: 13 March 2004
Proposed: Benson Farb
Seconded: Jean-Pierre Otal, Shigeyuki Morita
Authors
Erwan Lanneau
Institut de mathématiques de Luminy
Case 907, 163 Avenue de Luminy
F-13288 Marseille Cedex 9
France