{"paper":{"title":"The cohomology ring of the GKM graph of a flag manifold of classical type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hiroaki Ishida, Mikiya Masuda, Yukiko Fukukawa","submitted_at":"2011-04-11T02:55:30Z","abstract_excerpt":"If a closed smooth manifold $M$ with an action of a torus $T$ satisfies certain conditions, then a labeled graph $\\mG_M$ with labeling in $H^2(BT)$ is associated with $M$, which encodes a lot of geometrical information on $M$. For instance, the \"graph cohomology\" ring $\\mHT^*(\\mG_M)$ of $\\mG_M$ is defined to be a subring of $\\bigoplus_{v\\in V(\\mG_M)}H^*(BT)$, where $V(\\mG_M)$ is the set of vertices of $\\mG_M$, and is known to be often isomorphic to the equivariant cohomology $H^*_T(M)$ of $M$. In this paper, we determine the ring structure of $\\mHT^*(\\mG_M)$ with $\\Z$ (resp. $\\Z[1/2]$) coeffic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.1832","kind":"arxiv","version":3},"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"}