{"paper":{"title":"A geometric interpretation of the homotopy groups of the cobordism category","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Anne Marie Svane, Marcel B\\\"okstedt","submitted_at":"2012-08-16T13:54:02Z","abstract_excerpt":"The classifying space of the embedded cobordism category has been identified in by Galatius, Tillmann, Madsen, and Weiss as the infinite loop space of a certain Thom spectrum. This identifies the set of path components with the classical cobordism group. In this paper, we give a geometric interpretation of the higher homotopy groups as certain cobordism groups where all manifolds are now equipped with a set of orthonormal sections in the tangent bundle. We also give a description of the fundamental group as a free group with a set of geometrically intuitive relations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.3370","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"}