{"paper":{"title":"Bi-Lipschitz geometry of contact orbits in the boundary of the nice dimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Maria Aparecida Soares Ruas, Saurabh Trivedi","submitted_at":"2017-11-04T13:36:06Z","abstract_excerpt":"Mather proved that the smooth stability of smooth maps between manifolds is a generic condition if and only if the pair of dimensions of the manifolds are 'nice dimensions' while topologically stability is a generic condition in any pair of dimensions. And, by a result of du Plessis and Wall $C^1$-stability is also a generic condition precisely in the nice dimensions. We address the question of bi-Lipschitz stability in this article. We prove that the Thom-Mather stratification is bi-Lipschitz contact invariant in the boundary of the nice dimensions. This is done in two steps: first we explici"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.01435","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"}