{"paper":{"title":"Strongly minimal PD4-complexes","license":"","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Jonathan A. Hillman","submitted_at":"2007-12-07T02:09:30Z","abstract_excerpt":"We consider the homotopy types of $PD_4$-complexes $X$ with fundamental group $\\pi$ such that $c.d.\\pi=2$ and $\\pi$ has one end. Let $\\beta=\\beta_2(\\pi;F_2)$ and $w=w_1(X)$. Our main result is that (modulo two technical conditions on $(\\pi,w)$) there are at most $2^\\beta$ orbits of $k$-invariants determining \"strongly minimal\" complexes (i.e., those with homotopy intersection pairing $\\lambda_X$ trivial). The homotopy type of a $PD_4$-complex $X$ with $\\pi$ a $PD_2$-group is determined by $\\pi$, $w$, $\\lambda_X$ and the $v_2$-type of $X$. Our result also implies that Fox's 2-knot with metabeli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0712.1069","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"}