{"paper":{"title":"Perverse Sheaves and Knot Contact Homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT","math.KT","math.RT"],"primary_cat":"math.AT","authors_text":"Alimjon Eshmatov, Wai-kit Yeung, Yuri Berest","submitted_at":"2016-10-07T22:27:58Z","abstract_excerpt":"In this paper, which is mostly a research announcement, we give a new algebraic construction of knot contact homology in the sense of L. Ng [Ng05a]. For a link $L$ in $ {\\mathbb R}^3 $, we define a differential graded (DG) $k$-category $ \\tilde{\\mathscr A} $ with finitely many objects, whose quasi-equivalence class is a topological invariant of $ L $. In the case when $L$ is a knot, the endomorphism algebra of a distinguished object of $ \\tilde{\\mathscr A} $ coincides with the fully noncommutative knot DGA as defined by Ekholm, Etnyre, Ng and Sullivan in [EENS13a]. The input of our constructio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02438","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"}