{"paper":{"title":"Lin-Wang type formula for the Haefliger invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Keiichi Sakai","submitted_at":"2014-05-08T14:43:07Z","abstract_excerpt":"In this paper we study the Haefliger invariant for long embeddings $\\mathbb{R}^{4k-1}\\hookrightarrow\\mathbb{R}^{6k}$ in terms of the self-intersections of their projections to $\\mathbb{R}^{6k-1}$, under the condition that the projection is a generic long immersion $\\mathbb{R}^{4k-1}\\looparrowright\\mathbb{R}^{6k-1}$. We define the notion of \"crossing changes\" of the embeddings at the self-intersections and describe the change of the isotopy classes under crossing changes using the linking numbers of the double point sets in $\\mathbb{R}^{4k-1}$. This formula is a higher-dimensional analogue to t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1947","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"}