{"paper":{"title":"A combinatorial model for the path fibration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Manuel Rivera, Samson Saneblidze","submitted_at":"2017-06-03T17:36:45Z","abstract_excerpt":"We introduce the abstract notion of a necklical set in order to describe a functorial combinatorial model of the path fibration over the geometric realization of a path connected simplicial set. In particular, to any path connected simplicial set $X$ we associate a necklical set $\\widehat{\\mathbf{\\Omega}}X$ such that its geometric realization $|\\widehat{\\mathbf{\\Omega}}X|$, a space built out of gluing cubical cells, is homotopy equivalent to the based loop space on $|X|$ and the differential graded module of chains $C_*(\\widehat{\\mathbf{\\Omega}}X)$ is a differential graded associative algebra "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.00983","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":""},"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"}