{"paper":{"title":"Mirror links have dual odd and generalized Khovanov homology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GT","authors_text":"Krzysztof K. Putyra, Wojciech Lubawski","submitted_at":"2014-07-22T19:49:55Z","abstract_excerpt":"We show that the generalized Khovanov homology, defined by the second author in the framework of chronological cobordisms, admits a grading by the group $\\mathbb{Z}\\times\\mathbb{Z}_2$, in which all homogeneous summands are isomorphic to the unified Khovanov homology defined over the ring $\\mathbb{Z}_{\\pi}:=\\mathbb{Z}[\\pi]/(\\pi^2-1)$ (here, setting $\\pi$ to $\\pm 1$ results either in even or odd Khovanov homology). The generalized homology has $\\Bbbk := \\mathbb{Z}[X,Y,Z^{\\pm 1}]/(X^2=Y^2=1)$ as coefficients, and the above implies that most of automorphisms of $\\Bbbk$ fix the isomorphism class of"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.5987","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"}