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

By Artur Avila, A. Eskin, Martin Möller. 2012

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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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/5a0ed8e57e91a98f03724d61a488781ec4a2161e