{"paper":{"title":"A theory of characteristic currents associated with a singular connection","license":"","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"H. Blaine Jr. Lawson, Reese Harvey","submitted_at":"1994-07-01T00:00:00Z","abstract_excerpt":"This note announces a general construction of characteristic currents for singular connections on a vector bundle. It develops, in particular, a Chern-Weil-Simons theory for smooth bundle maps $\\alpha : E \\rightarrow F$ which, for smooth connections on $E$ and $F$, establishes formulas of the type $$ \\phi \\ = \\ \\text{\\rm Res}_{\\phi}\\Sigma_{\\alpha} + dT. $$ Here $\\phi$ is a standard charactersitic form, $\\text{Res}_{\\phi}$ is an associated smooth ``residue'' form computed canonically in terms of curvature, $\\Sigma_{\\alpha}$ is a rectifiable current depending only on the singular structure of $\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9407216","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"}