{"paper":{"title":"On The Homflypt Skein Module of S^1 x S^2","license":"","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Jianyuan Zhong, Patrick M. Gilmer","submitted_at":"2000-07-20T22:48:49Z","abstract_excerpt":"Let $k$ be a subring of the field of rational functions in $x, v, s$ which contains $x^{\\pm 1}, v^{\\pm 1}, s^{\\pm 1}$. If $M$ is an oriented 3-manifold, let $S(M)$ denote the Homflypt skein module of $M$ over $k$. This is the free $k$-module generated by isotopy classes of framed oriented links in $M$ quotiented by the Homflypt skein relations: (1) $x^{-1}L_{+}-xL_{-}=(s-s^{-1})L_{0}$; (2) $L$ with a positive twist $=(xv^{-1})L$; (3) $L\\sqcup O=(\\frac{v-v^{-1}}{s-s^{-1}})L$ where $O$ is the unknot. We give two bases for the relative Homflypt skein module of the solid torus with 2 points in the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0007125","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"}