{"paper":{"title":"Cohomological consequences of (almost) free torus actions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Manuel Amann","submitted_at":"2012-04-27T17:31:51Z","abstract_excerpt":"The long-standing Halperin--Carlsson conjecture (basically also known as the toral rank conjecture) states that the sum of all Betti numbers of a well-behaved space $X$ (with cohomology taken with coefficients in the cyclic group $\\zz_p$ in characteristic $p>0$ respectively with rational coefficients for characteristic 0) is at least $2^n$ where $n$ is the rank of an $n$-torus $\\zz_p \\times \\stackrel{(n)}...\\times \\zz_p$ (in characteristic $p>0$) respectively $\\s^1 \\times \\stackrel{(n)}...\\times \\s^1$ (in characteristic 0) acting freely (characteristic $p>0$) respectively almost freely (charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.6276","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"}