{"paper":{"title":"Anomalous partially hyperbolic diffeomorphisms I: dynamically coherent examples","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Christian Bonatti, Kamlesh Parwani, Rafael Potrie","submitted_at":"2014-11-05T10:43:22Z","abstract_excerpt":"We build an example of a non-transitive, dynamically coherent partially hyperbolic diffeomorphism $f$ on a closed $3$-manifold with exponential growth in its fundamental group such that $f^n$ is not isotopic to the identity for all $n\\neq 0$. This example contradicts a conjecture in \\cite{HHU}. The main idea is to consider a well-understood time-$t$ map of a non-transitive Anosov flow and then carefully compose with a Dehn twist."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.1221","kind":"arxiv","version":2},"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"}