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

Abstract

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.

23 pages. To appear in Crelle's journal

References in corpus (3)

• Invariant and stationary measures for the SL(2,R) action on Moduli space
• An example of a Teichmuller disk in genus 4 with degenerate Kontsevich-Zorich spectrum
• Small eigenvalues of the Laplacian for algebraic measures in moduli space, and mixing properties of the Teichmüller flow

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