{"paper":{"title":"Coverings and fundamental groups: a new approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GN","authors_text":"Jerzy Dydak","submitted_at":"2011-08-15T18:35:40Z","abstract_excerpt":"The traditional approach of defining the fundamental group first and then constructing universal coverings works well only for the class of Poincar\\' e spaces. For general spaces there were several attempts to define generalized coverings (see \\cite{BP3}, \\cite{BDLM}, and \\cite{FisZas}), yet there is no general theory so far that covers all path connected spaces. In this paper we plan to remedy that by changing the order of things: we define the universal covering first and its group of deck transformations is the new fundamental group of the base space.\n  The basic idea is that a non-trivial "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3253","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"}