{"paper":{"title":"A curvature form for pseudoconnections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"C.A. Morales, M. Vilches","submitted_at":"2014-09-11T15:39:04Z","abstract_excerpt":"We obtain the curvature form $F^\\nabla=P\\circ d^\\nabla\\circ\\nabla-d^\\nabla\\circ P\\circ\\nabla+d^\\nabla\\circ\\nabla\\circ P$ for a vector bundle pseudoconnection $\\nabla$, where $d^\\nabla$ is the exterior derivative associated to $\\nabla$. We use $F^\\nabla$ to obtain the curvature of $\\nabla$. We also prove that $F^\\nabla=0$ is a necessary (but not sufficient) condition for $d^\\nabla$ to be a chain complex. Instead we prove that $F^\\nabla=0$ and $d^\\nabla\\circ d^\\nabla\\circ\\nabla=0$ are necessary and sufficient conditions for $d^\\nabla$ to be a {\\em chain $2$-complex}, i.e., $d^\\nabla\\circ d^\\nabl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.3479","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"}