{"paper":{"title":"Generalised geometric weak conjecture on spherical classes and non-factorisation of Kervaire invariant one elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hadi Zare","submitted_at":"2015-12-07T13:48:53Z","abstract_excerpt":"This paper is on the Curtis conjecture. We show that the image of the Hurewicz homomorhism $h:\\pi_*Q_0S^0\\to H_*(Q_0S^0;\\mathbb{Z})$, when restricted to product of positive dimensional elements, is determined by $\\mathbb{Z}\\{h(\\eta^2),h(\\nu^2),h(\\sigma^2)\\}$. Localised at $p=2$, this proves a geometric version of a result of Hung and Peterson for the Lannes-Zarati homomorphism. We apply this to show that, for $p=2$ and $G=O(1)$ or any prime $p$ and $G$ any compact Lie group with Lie algebra $\\mathfrak{g}$ so that $\\dim\\mathfrak{g}>0$, the composition $${_p\\pi_*}Q\\Sigma^{n\\dim\\mathfrak{g}}BG_+^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.02040","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"}