{"paper":{"title":"Generic Pseudogroups on (C,0) and the Topology of Leaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Helena Reis, Jean-Fran\\c{c}ois Mattei, Julio C. Rebelo","submitted_at":"2011-11-09T23:27:20Z","abstract_excerpt":"We show that generically a pseudogroup generated by holomorphic diffeomorphisms defined about $0 \\in \\mathbb{C}$ is free in the sense of pseudogroups even if the class of conjugacy of the generators is fixed. This result has a number of consequences on the topology of leaves for a (singular) holomorphic foliation defined on a neighborhood of an invariant curve. In particular in the classical and simplest case arising from local foliations possessing a unique separatrix that is given by a cusp of the form $\\{y^2-x^{2k+1}=0\\}$, our results allow us to settle the problem of showing that a generic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2364","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"}