{"paper":{"title":"Lyapunov spectrum of invariant subbundles of the Hodge bundle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anton Zorich, Carlos Matheus, Giovanni Forni","submitted_at":"2011-12-02T01:47:48Z","abstract_excerpt":"We study the Lyapunov spectrum of the Kontsevich--Zorich cocycle on $SL(2,\\mathbb{R})$-invariant subbundles of the Hodge bundle over the support of a $SL(2,\\mathbb{R})$-invariant probability measure on the moduli space of Abelian differentials.\n  In particular, we prove formulas for partial sums of Lyapunov exponents in terms of the second fundamental form (or Kodaira--Spencer map) of the Hodge bundle with respect to Gauss--Manin connection and investigate the relations between the central {Oseldets} subbundle and the kernel of the second fundamental form. We illustrate our conclusions in two "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0370","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}