{"paper":{"title":"Infinite-dimensionality of the rational homotopy groups of the space of long embeddings of codimension 2","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.AT","authors_text":"Daiki Irikura","submitted_at":"2026-06-01T08:42:47Z","abstract_excerpt":"In this paper, we study the space of compactly supported embeddings between Euclidean spaces, $\\mathrm{Emb}_c(\\mathbb{R}^j, \\mathbb{R}^n)$. By utilizing hairy graphs, we construct elements in the homotopy groups $\\pi_{\\bullet}(\\overline{\\mathrm{Emb}}_c(\\mathbb{R}^j, \\mathbb{R}^{n})) \\otimes \\mathbb{Q}$ corresponding to certain uni-trivalent graphs in the model. We then prove that these elements are nontrivial. Consequently, we show that the rational homotopy groups of $\\mathrm{Emb}_c(\\mathbb{R}^{n-2}, \\mathbb{R}^n)$ are infinite-dimensional in infinitely many degrees when $n \\ge 5$ is odd."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.01903","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.01903/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}