{"paper":{"title":"Algebraic links in the Poincar\\'e sphere and the Alexander polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"A. Campillo, F. Delgado, S. M. Gusein-Zade","submitted_at":"2018-04-10T09:44:10Z","abstract_excerpt":"The Alexander polynomial in several variables is defined for links in three-dimensional homology spheres, in particular, in the Poincar\\'e sphere: the intersection of the surface $S=\\{(z_1,z_2,z_3)\\in {\\mathbb C}^3: z_1^5+z_2^3+z_3^2=0\\}$ with the 5-dimensional sphere ${\\mathbb S}_{\\varepsilon}^5=\\{(z_1,z_2,z_3)\\in {\\mathbb C}^3: \\vert z_1\\vert^2+\\vert z_2\\vert^2+\\vert z_3\\vert^2=\\varepsilon^2\\}$. An algebraic link in the Poincar\\'e sphere is the intersection of a germ $(C,0)\\subset (S,0)$ of a complex analytic curve in $(S,0)$ with the sphere ${\\mathbb S}_{\\varepsilon}^3$ of radius $\\varepsil"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1804.03419","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"}