{"paper":{"title":"What's wrong with the growth of simple closed geodesics on nonorientable hyperbolic surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Matthieu Gendulphe","submitted_at":"2017-06-27T11:54:48Z","abstract_excerpt":"A celebrated result of Mirzakhani states that, if $(S,m)$ is a finite area \\emph{orientable} hyperbolic surface, then the number of simple closed geodesics of length less than $L$ on $(S,m)$ is asymptotically equivalent to a positive constant times $L^{\\dim\\mathcal{ML}(S)}$, where $\\mathcal{ML}(S)$ denotes the space of measured laminations on $S$. We observed on some explicit examples that this result does not hold for \\emph{nonorientable} hyperbolic surfaces. The aim of this article is to explain this surprising phenomenon. Let $(S,m)$ be a finite area \\emph{nonorientable} hyperbolic surface."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.08798","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"}