{"paper":{"title":"Fiber Strong Shape Theory for Topological Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Ruslan Tsinaridze, Vladimer Baladze","submitted_at":"2017-03-30T09:19:10Z","abstract_excerpt":"In the paper we construct and develop a fiber strong shape theory for arbitrary spaces over fixed metrizable space $\\Bo$. Our approach is based on the method of Marde\\v{s}i\\'{c}-Lisica and instead of resolutions, introduced by Marde\\v{s}i\\'{c}, their fiber preserving analogues are used. The fiber strong shape theory yields the classification of spaces over $\\Bo$ which is coarser than the classification of spaces over $\\Bo$ induced by fiber homotopy theory, but is finer than the classification of spaces over $\\Bo$ given by usual fiber shape theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.10374","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"}