{"paper":{"title":"Small covers and the equivariant bordism classification of 2-torus manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.RA","math.RT"],"primary_cat":"math.AT","authors_text":"Qiangbo Tan, Zhi L\\\"u","submitted_at":"2010-08-12T17:23:08Z","abstract_excerpt":"Associated with the Davis-Januszkiewicz theory of small covers, this paper deals with the theory of 2-torus manifolds from the viewpoint of equivariant bordism. We define a differential operator on the \"dual\" algebra of the unoriented $G_n$-representation algebra introduced by Conner and Floyd, where $G_n=(\\Z_2)^n$. With the help of $G_n$-colored graphs (or mod 2 GKM graphs), we may use this differential operator to give a very simple description of tom Dieck-Kosniowski-Stong localization theorem in the setting of 2-torus manifolds. We then apply this to study the $G_n$-equivariant unoriented "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1008.2166","kind":"arxiv","version":4},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}