{"paper":{"title":"Free actions on products of real projective spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ergun Yalcin","submitted_at":"2025-06-04T15:32:40Z","abstract_excerpt":"We prove that if $G=(\\mathbb{Z}/2)^r$ acts freely and cellularly on a finite-dimensional CW-complex $X$ homotopy equivalent to $\\mathbb{R}P ^{n_1} \\times \\cdots \\times \\mathbb{R} P ^{n_k}$ with trivial action on the mod-$2$ cohomology, then $r \\leq \\mu (n_1)+ \\cdots + \\mu(n_k )$ where for each integer $n\\geq 0$, $\\mu (n)=0$ if $n$ is even, $\\mu(n)=1$ if $n\\equiv 1$ mod 4, and $\\mu(n)=2$ if $n\\equiv 3$ mod 4. This proves a homotopy-theoretic version of a conjecture of Cusick."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.04067","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.04067/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}