{"paper":{"title":"The higher twisted index theorem for foliations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.KT","authors_text":"Alexander Gorokhovsky, Eric Leichtnam, Moulay-Tahar Benameur","submitted_at":"2016-07-14T18:55:33Z","abstract_excerpt":"Given a gerbe $L$, on the holonomy groupoid $\\mathcal G$ of the foliation $(M, \\mathcal F)$, whose pull-back to $M$ is torsion, we construct a Connes $\\Phi$-map from the twisted Dupont-Sullivan bicomplex of $\\mathcal G$ to the cyclic complex of the $L$-projective leafwise smoothing operators on $(M, \\mathcal F)$. Our construction allows to couple the $K$-theory analytic indices of $L$-projective leafwise elliptic operators with the twisted cohomology of $B\\mathcal G$ producing scalar higher invariants. Finally by adapting the Bismut-Quillen superconnection approach, we compute these higher twi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1607.04248","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":""},"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"}