{"paper":{"title":"Embeddings of homology equivalent manifolds with boundary","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"A. Skopenkov, D. Goncalves","submitted_at":"2012-07-05T18:55:37Z","abstract_excerpt":"We prove a theorem on equivariant maps implying the following two corollaries:\n  (1) Let N and M be compact orientable n-manifolds with boundaries such that M\\subset N, the inclusion M\\to N induces an isomorphism in integral cohomology, both M and N have (n-d-1)-dimensional spines and m > max {n+2, (3n+1-d)/2} . Then the restriction-induced map E^m(N)\\to E^m(M) is bijective. Here E^m(X) is the set of embeddings X\\to R^m up to isotopy (in the PL or smooth category).\n  (2) For a 3-manifold N with boundary whose integral homology groups are trivial and such that N\\not\\cong D^3 (or for its special"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.1326","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"}