{"paper":{"title":"Freudenthal theorem and spherical classes in $H_*QS^0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hadi Zare","submitted_at":"2018-01-18T06:09:00Z","abstract_excerpt":"This note is on spherical classes in $H_*(QS^0;k)$ when $k=\\mathbb{Z},\\mathbb{Z}/p$ with a special focus on the case of $p=2$ related to Curtis conjecture. We apply Freudenthal theorem to prove a vanishing result for the Hurewicz image of elements in ${\\pi_*^s}$ that factor through certain finite spectra. Either in $p$-local or $p$-complete settings, this immediately implies that elements of well known infinite families in ${_p\\pi_*^s}$, such as Mahowaldean families, map trivially under the unstable Hurewicz homomorphism ${_p\\pi_*^s}\\simeq{_p\\pi_*}QS^0\\to H_*(QS^0;\\mathbb{Z}/p)$. We also obser"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06427","kind":"arxiv","version":2},"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"}