{"paper":{"title":"On the non-existence of certain branched covers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.CV"],"primary_cat":"math.GT","authors_text":"Juan Souto, Pekka Pankka","submitted_at":"2010-08-10T11:33:03Z","abstract_excerpt":"We prove that while there are maps $\\bT^4\\to\\#^3(\\bS^2\\times\\bS^2)$ of arbitrarily large degree, there is no branched cover from $4$-torus to $\\#^3(\\bS^2\\times \\bS^2)$. More generally, we obtain that, as long as $N$ satisfies a suitable cohomological condition, any $\\pi_1$-surjective branched cover $\\bT^n \\to N$ is a homeomorphism."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.1694","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"}