{"paper":{"title":"Geometric approach to stable homotopy groups of spheres II. The Kervaire invariant","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Petr M. Akhmet'ev","submitted_at":"2010-11-26T06:50:30Z","abstract_excerpt":"A solution to the Kervaire invariant problem is presented. We introduce the concepts of abelian structure on skew-framed immersions, bicyclic structure on $\\Z/2^{[3]}$--framed immersions, and quaternionic-cyclic structure on $\\Z/2^{[4]}$--framed immersions. Using these concepts, we prove that for sufficiently large $n$, $n=2^{\\ell}-2$, an arbitrary skew-framed immersion in Euclidean $n$-space $\\R^n$ has zero Kervaire invariant. Additionally, for $\\ell \\ge 12$ (i.e., for $n \\ge 4094$) an arbitrary skew-framed immersion in Euclidean $n$-space $\\R^n$ has zero Kervaire invariant if this skew-frame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.5717","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"}