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arXiv:1209.2854 [math.DS]AbstractReferencesReviewsResources

Symplectic and Isometric SL(2,R) invariant subbundles of the Hodge bundle

Artur Avila, Alex Eskin, Martin Moeller

Published 2012-09-13, updated 2014-12-04Version 2

Suppose N is an affine SL(2,R)-invariant submanfold of the moduli space of pairs (M,w) where M is a curve, and w is a holomorphic 1-form on M. We show that the Forni bundle of N (i.e. the maximal SL(2,R)-invariant isometric subbundle of the Hodge bundle of N) is always flat and is always orthogonal to the tangent space of N. As a corollary, it follows that the Hodge bundle of N is semisimple.

Comments: 23 pages. To appear in Crelle's journal
Categories: math.DS, math.AG, math.GT
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