{"paper":{"title":"Periodic Cyclic Homology and Equivariant Gerbes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.DG"],"primary_cat":"math.KT","authors_text":"Jean-Louis Tu, Ping Xu","submitted_at":"2015-04-30T02:59:29Z","abstract_excerpt":"This paper is our first step in establishing a de Rham model for equivariant twisted $K$-theory using machinery from noncommutative geometry. Let $G$ be a compact Lie group, $M$ a compact manifold on which $G$ acts smoothly. For any $\\alpha \\in H^3_G (M, {\\mathbb Z})$ we introduce a notion of localized equivariant twisted cohomology $H^\\bullet ({\\bar{\\Omega}}^\\bullet (M, G, L)_g, d^\\alpha_{G^g})$, indexed by $g\\in G$. We prove that there exists a natural family of chain maps, indexed by $g\\in G$, inducing a family of morphisms from the equivariant periodic cyclic homology $HP^G_\\bullet ( C^\\in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.08064","kind":"arxiv","version":1},"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"}