{"paper":{"title":"Lower bounds for regular genus and gem-complexity of PL 4-manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Biplab Basak, Maria Rita Casali","submitted_at":"2015-04-03T08:07:16Z","abstract_excerpt":"Within crystallization theory, two interesting PL invariants for $d$-manifolds have been introduced and studied, namely {\\it gem-complexity} and {\\it regular genus}. In the present paper we prove that, for any closed connected PL $4$-manifold $M$, its gem-complexity $\\mathit{k}(M)$ and its regular genus $ \\mathcal G(M)$ satisfy: $$\\mathit{k}(M) \\ \\geq \\ 3 \\chi (M) + 10m -6 \\ \\ \\ \\text{and} \\ \\ \\ \\mathcal G(M) \\ \\geq \\ 2 \\chi (M) + 5m -4,$$ where $rk(\\pi_1(M))=m.$ These lower bounds enable to strictly improve previously known estimations for regular genus and gem-complexity of product 4-manifol"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.00771","kind":"arxiv","version":2},"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"}