{"paper":{"title":"Discrete degree of symmetry of manifolds","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.GT"],"primary_cat":"math.AT","authors_text":"Ignasi Mundet i Riera","submitted_at":"2021-12-10T15:31:10Z","abstract_excerpt":"We define the discrete degree of symmetry $disc-sym(X)$ of a closed $n$-manifold $X$ as the biggest $m\\geq 0$ such that $X$ supports an effective action of $({\\mathbf Z}/r)^m$ for arbitrarily big values of $r$. We prove that if $X$ is connected then $disc-sym(X)\\leq 3n/2$. We propose the question of whether for every closed connected $n$-manifold $X$ the inequality $disc-sym(X)\\leq n$ holds true, and whether the only closed connected $n$-manifold $X$ for which $disc-sym(X)=n$ is the torus $T^n$. We prove partial results providing evidence for an affirmative answer to this question."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2112.05599","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2112.05599/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"}