{"paper":{"title":"A combinatorial model for the free loop fibration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.QA"],"primary_cat":"math.AT","authors_text":"Manuel Rivera, Samson Saneblidze","submitted_at":"2017-12-06T14:22:15Z","abstract_excerpt":"We introduce the abstract notion of a closed necklical set in order to describe a functorial combinatorial model of the free loop fibration $\\Omega Y\\rightarrow \\Lambda Y\\rightarrow Y$ over the geometric realization $Y=|X|$ of a path connected simplicial set $X.$ In particular, to any path connected simplicial set $X$ we associate a closed necklical set $\\widehat{\\mathbf{\\Lambda}}X$ such that its geometric realization $|\\widehat{\\mathbf{\\Lambda}}X|$, a space built out of gluing \"freehedrical\" and \"cubical\" cells, is homotopy equivalent to the free loop space $\\Lambda Y$ and the differential gr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.02644","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"}