{"paper":{"title":"Abe homotopy classification of topological excitations under the topological influence of vortices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.other","hep-th","math.MP"],"primary_cat":"math-ph","authors_text":"Masahito Ueda, Michikazu Kobayashi, Muneto Nitta, Shingo Kobayashi, Yuki Kawaguchi","submitted_at":"2011-10-07T10:23:03Z","abstract_excerpt":"Topological excitations are usually classified by the $n$th homotopy group $\\pi_n$. However, for topological excitations that coexist with vortices, there are case in which an element of $\\pi_n$ cannot properly describe the charge of a topological excitation due to the influence of the vortices. This is because an element of $\\pi_n$ corresponding to the charge of a topological excitation may change when the topological excitation circumnavigates a vortex. This phenomenon is referred to as the action of $\\pi_1$ on $\\pi_n$. In this paper, we show that topological excitations coexisting with vort"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1478","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"}