{"paper":{"title":"Invariants of singular sets of smooth maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Rustam Sadykov","submitted_at":"2010-04-03T18:41:36Z","abstract_excerpt":"A singular point of a smooth map F: M -> N of manifolds is a point in M at which the rank of the differential dF is less than the minimum of dimensions of M and N. The classical invariant of the set S of singular points of F of a given type is defined by taking the fundamental class [\\bar{S}]\\in H_*(M) of the closure of S. We introduce and study new invariants of singular sets for which the classical invariants may not be defined, i.e., for which \\bar{S} may not possess the fundamental class. The simplest new invariant is defined by carefully choosing the fundamental class of the intersection "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1004.0460","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"}