{"paper":{"title":"Cohomology classes represented by measured foliations, and Mahler's question for interval exchanges","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Barak Weiss, Yair N. Minsky","submitted_at":"2011-02-23T12:04:26Z","abstract_excerpt":"A translation surface on (S, \\Sigma) gives rise to two transverse measured foliations \\FF, \\GG on S with singularities in \\Sigma, and by integration, to a pair of cohomology classes [\\FF], \\, [\\GG] \\in H^1(S, \\Sigma; \\R). Given a measured foliation \\FF, we characterize the set of cohomology classes \\B for which there is a measured foliation \\GG as above with \\B = [\\GG]. This extends previous results of Thurston and Sullivan.\n  We apply this to two problems: unique ergodicity of interval exchanges and flows on the moduli space of translation surfaces. For a fixed permutation \\sigma \\in \\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4719","kind":"arxiv","version":1},"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"}