{"paper":{"title":"A Hurewicz Theorem for $RO(C_2)$-graded Equivariant Homology Governed by Vector Fields on Spheres","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AT","authors_text":"Albert Jinghui Yang, Guchuan Li, Manyi Guo, Shangjie Zhang, Sihao Ma, Yuchen Wu, Yunze Lu, Zhouli Xu","submitted_at":"2026-05-25T21:13:28Z","abstract_excerpt":"We determine the $RO(C_2)$-graded Hurewicz images of the $C_2$-equivariant Eilenberg--MacLane spectra $H\\underline{\\mathbb F_2}$, $H\\underline{\\mathbb Z}$ and $H\\underline{A}$, where $\\underline{\\mathbb F_2}$ and $\\underline{\\mathbb Z}$ denote the constant Mackey functors with values in $\\mathbb F_2$ and $\\mathbb Z$, respectively, and $\\underline A$ denotes the Burnside Mackey functor.\n  Surprisingly, the answer is closely tied to the problem of vector fields on spheres: the element $\\frac{\\theta}{\\rho^k\\tau^n}$ in the negative cone of the homotopy groups of $H\\underline{\\mathbb F_2}$ lies in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.26334","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2605.26334/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}