{"paper":{"title":"Algorithmic solvability of the lifting-extension problem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.CG"],"primary_cat":"math.AT","authors_text":"Luk\\'a\\v{s} Vok\\v{r}\\'inek, Marek Kr\\v{c}\\'al, Martin \\v{C}adek","submitted_at":"2013-07-24T14:58:03Z","abstract_excerpt":"Let $X$ and $Y$ be finite simplicial sets (e.g. finite simplicial complexes), both equipped with a free simplicial action of a finite group $G$. Assuming that $Y$ is $d$-connected and $\\dim X\\le 2d$, for some $d\\geq 1$, we provide an algorithm that computes the set of all equivariant homotopy classes of equivariant continuous maps $|X|\\to|Y|$; the existence of such a map can be decided even for $\\dim X\\leq 2d+1$. For fixed $G$ and $d$, the algorithm runs in polynomial time. This yields the first algorithm for deciding topological embeddability of a $k$-dimensional finite simplicial complex int"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.6444","kind":"arxiv","version":4},"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"}