{"paper":{"title":"Knot contact homology, string topology, and the cord algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Janko Latschev, Kai Cieliebak, Lenhard Ng, Tobias Ekholm","submitted_at":"2016-01-09T23:58:10Z","abstract_excerpt":"The conormal Lagrangian $L_K$ of a knot $K$ in $\\mathbb{R}^3$ is the submanifold of the cotangent bundle $T^* \\mathbb{R}^3$ consisting of covectors along $K$ that annihilate tangent vectors to $K$. By intersecting with the unit cotangent bundle $S^* \\mathbb{R}^3$, one obtains the unit conormal $\\Lambda_K$, and the Legendrian contact homology of $\\Lambda_K$ is a knot invariant of $K$, known as knot contact homology. We define a version of string topology for strings in $\\mathbb{R}^3 \\cup L_K$ and prove that this is isomorphic in degree 0 to knot contact homology. The string topology perspective"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.02167","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"}