{"paper":{"title":"Localization for nonabelian group actions","license":"","headline":"","cross_cats":["math.AG"],"primary_cat":"alg-geom","authors_text":"F.C. Kirwan, L.C. Jeffrey","submitted_at":"1993-07-06T22:55:00Z","abstract_excerpt":"Suppose $X$ is a compact symplectic manifold acted on by a compact Lie group $K$ (which may be nonabelian) in a Hamiltonian fashion, with moment map $\\mu: X \\to {\\rm Lie}(K)^*$ and Marsden-Weinstein reduction $\\xred = \\mu^{-1}(0)/K$. There is then a natural surjective map $\\kappa_0$ from the equivariant cohomology $H^*_K(X) $ of $X$ to the cohomology $H^*(\\xred)$. In this paper we prove a formula (Theorem 8.1, the residue formula) for the evaluation on the fundamental class of $\\xred$ of any $\\eta_0 \\in H^*(\\xred)$ whose degree is the dimension of $\\xred$, provided that $0$ is a regular value "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"alg-geom/9307001","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/alg-geom/9307001/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"}