{"paper":{"title":"On the relation between Dyer-Lashof algebra and the hit problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Hadi Zare","submitted_at":"2016-03-20T21:17:36Z","abstract_excerpt":"The aim of this note is to use geometric methods to study the hit problem of Peterson for $H_*\\mathbb{R} P^{\\times k}$ as well as the symmetric hit problem of Janfada and Wood for $H_*BO(k)$. We continue by exploring the applications of the results of \\cite{Zare-symmetric} on the $\\mathcal{A}$-annihilated generators of $H_*QX$ to obtain a family of generic `new' examples of $\\mathcal{A}$-annihilated in $H_*(\\mathbb{Z}\\times BO)$ and $H_*BO$, i.e. the case of stable symmetric hit problem, where an essential step is provided by the infinite loop space structure on $BO$ implied by the Bott period"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.06271","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"}