{"paper":{"title":"A lossless reduction of geodesics on supermanifolds to non-graded differential geometry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Matthias Kalus, St\\'ephane Garnier","submitted_at":"2014-06-23T11:29:46Z","abstract_excerpt":"Let $\\mathcal M= (M,\\mathcal O_\\mathcal M)$ be a smooth supermanifold with connection $\\nabla$ and Batchelor model $\\mathcal O_\\mathcal M\\cong\\Gamma_{\\Lambda E^\\ast}$. From $(\\mathcal M,\\nabla)$ we construct a connection on the total space of the vector bundle $E\\to{M}$. This reduction of $\\nabla$ is well-defined independently of the isomorphism $\\mathcal O_\\mathcal M \\cong \\Gamma_{\\Lambda E^\\ast}$. It erases information, but however it turns out that the natural identification of supercurves in $\\mathcal M$ (as maps from $ \\mathbb R^{1|1}$ to $\\mathcal M$) with curves in $E$ restricts to a 1 "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.5870","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"}