{"paper":{"title":"On the mod-2 cohomology of the product of the infinite lens space and the space of invariants in a generic degree","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Dang Vo Phuc","submitted_at":"2024-08-14T11:56:59Z","abstract_excerpt":"Let $\\mathbb S^{\\infty}/\\mathbb Z_2$ be the infinite lens space and $\\mathscr A$ be the Steenrod algebra over the binary field $\\mathbb F_2.$ The cohomology $H^{*}((\\mathbb S^{\\infty}/\\mathbb Z_2)^{\\oplus s}; \\mathbb F_2)$ is known to be isomorphic to the graded polynomial ring $\\mathcal {P}_s:= \\mathbb F_2[x_1, \\ldots, x_s]$ on $s$ generators of degree 1, viewed as an unstable $\\mathscr A$-module. The Kameko squaring operation $(\\widetilde {Sq^0_*})_{(s; N)}: (\\mathbb F_2\\otimes_{\\mathscr A} \\mathcal {P}_s)_{2N+s} \\longrightarrow (\\mathbb F_2\\otimes_{\\mathscr A} \\mathcal {P}_s)_{N}$ is rather"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2408.07485","kind":"arxiv","version":7},"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/2408.07485/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"}