{"paper":{"title":"On the Transverse Khovanov-Rozansky Homologies: Graded Module Structure and Stabilization","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.GT","authors_text":"Hao Wu","submitted_at":"2014-03-24T18:58:39Z","abstract_excerpt":"In arXiv:1308.3152, the author proved that the Khovanov-Rozansky homology $\\mathcal{H}_N$ with potential $ax^{N+1}$ is an invariant for transverse links in the standard contact $3$-sphere. In the current paper, we study the $\\mathbb{Z}_2 \\oplus \\mathbb{Z}^{\\oplus 3}$-graded $\\mathbb{Q}[a]$-module structure of $\\mathcal{H}_N$, which leads to better understanding of the effect of stabilization on $\\mathcal{H}_N$. As an application, we compute $\\mathcal{H}_N$ for all transverse unknots."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6083","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"}