{"paper":{"title":"On the homology description of equivariant unoriented bordism groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Bo Chen, Zhi L\\\"u","submitted_at":"2025-08-15T23:41:19Z","abstract_excerpt":"We construct a chain complex $\\mathfrak{B}$ based on a double complex derived from the universal complex $X(\\mathbb{Z}_2^n)$. It is shown that $\\mathfrak{B}$ has a nontrivial homology only in degree $n-2$, which is isomorphic to the equivariant unoriented bordism group $\\mathcal{Z}_{n+1}(\\mathbb{Z}_2^n)$ of all $(n+1)$-dimensional smooth closed $\\mathbb{Z}_2^n$-manifolds with isolated fixed points. By analyzing the spectral sequence of $\\mathfrak{B}$, we derive a dimension formula for $\\mathcal{Z}_{n+1}(\\mathbb{Z}_2^n)$ as a $\\mathbb{Z}_2$-vector space, which agrees with a recent result for $n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2508.11841","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/2508.11841/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"}