{"paper":{"title":"Eilenberg--Mac Lane Spaces for Topological Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.GR","authors_text":"Ged Corob Cook","submitted_at":"2018-03-06T18:46:13Z","abstract_excerpt":"The goal of this paper is to establish a topological version of the notion of an Eilenberg-Mac Lane space. If $X$ is a pointed topological space, $\\pi_1(X)$ has a natural topology coming from the compact-open topology on the space of maps $S^1 \\to X$. In general the construction does not produce a topological group because it is possible to create examples where the group multiplication $\\pi_1(X) \\times \\pi_1(X) \\to \\pi_1(X)$ is discontinuous. This failure to obtain a topological group has been noticed by others, for example Fabel. However, if we work in the category of compactly generated, we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.02333","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"}