{"paper":{"title":"A New Route to the Interpretation of Hopf Invariant","license":"","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Ji-rong Ren, Ran Li, Yi-Shi Duan","submitted_at":"2006-07-01T07:49:11Z","abstract_excerpt":"We discuss an object from algebraic topology, Hopf invariant, and reinterpret it in terms of the $\\phi$-mapping topological current theory. The main purpose in this paper is to present a new theoretical framework which can directly give the relationship between Hopf invariant and the linking numbers of the higher dimensional submanifolds of Euclidean space $R^{2n-1}$.\n  For the sake of this purpose we introduce a topological tensor current which can naturally deduce the $(n-1)$ dimensional topological defect in $R^{2n-1}$ space. If these $(n-1)$ dimensional topological defects are closed orien"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0607001","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math-ph/0607001/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}