{"paper":{"title":"Finite abelian group actions on weakly Lefschetz cohomologically symplectic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ignasi Mundet i Riera","submitted_at":"2025-07-30T09:51:59Z","abstract_excerpt":"We study finite abelian group actions on weakly Lefschetz cohomologically symplectic (WLS) manifolds, a collection of manifolds that includes all compact connected Kaehler manifolds. We prove that for any WLS manifold $X$ there exists a number $C$ such that, for any integer $m\\geq C$, if $({\\mathbf Z}/m)^k$ acts freely on $X$, then $\\sum_j b_j(X;{\\mathbf Q})\\geq 2^k$.\n  We also prove a structure theorem for effective actions on WLS manifolds of $({\\mathbf Z}/p)^r$, where $p$ is a big enough prime, analogous to some results for tori of Lupton and Oprea, and we find bounds on the discrete degree"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2507.22525","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/2507.22525/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"}