{"paper":{"title":"On eigen-structures for pseudoAnosov maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.DS","authors_text":"Philip Boyland","submitted_at":"2010-09-15T14:06:55Z","abstract_excerpt":"We investigate various structures associated with the hyperbolic Markov and homological spectra of a pseudoAnosov map $\\phi$ on a surface. Each unstable eigenvalue of the action of $\\phi$ on first cohomolgy yields an eigen-cocycle that is transverse and holonomy invariant to the stable foliation $\\mathcal{F}^s$ of $\\phi$. Each unstable eigenvalue $\\mu$ of a Markov transition matrix for $\\phi$ yields a holonomy invariant additive function $G$ on transverse arcs to $\\cF^s$ with $\\phi^* G = \\mu G$. Except when $\\mu$ is the dilation of $\\phi$, these transverse arc functions do not yield measures, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2932","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"}