{"paper":{"title":"Transverse fundamental group and projected embeddings","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Sergey A. Melikhov","submitted_at":"2015-05-04T00:53:23Z","abstract_excerpt":"For a generic degree d smooth map f: N^n -> M^n we introduce its \"transverse fundamental group\" \\pi(f), which reduces to \\pi_1(M) in the case where f is a covering, and in general admits a monodromy homomorphism \\pi(f) -> S_{|d|}; nevertheless, we show that \\pi(f) can be non-trivial already for rather simple degree 1 maps S^n -> S^n.\n  We apply \\pi(f) to the problem of lifting f to an embedding N -> M x R^2: for such a lift to exist, the monodromy \\pi(f) -> S_{|d|} must factor through the group of concordance classes of |d|-component string links. At least if |d|<7, this requires \\pi(f) to be "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.00505","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"}