{"paper":{"title":"Banach algebras, Samelson products, and the Wang Differential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.OA","authors_text":"Claude L. Schochet","submitted_at":"2012-09-19T01:40:59Z","abstract_excerpt":"Supppose given a principal $G$ bundle $\\zeta : P \\to S^k$ (with $k \\geq 2$) and a Banach algebra $B$ upon which $G$ acts continuously. Let \\[ \\zeta\\otimes B : \\qquad P \\times_G B \\longrightarrow S^k \\] denote the associated bundle and let \\[ A_{\\zeta\\otimes B} = \\Gamma (S^k, P \\times_G B) \\] denote the associated Banach algebra of sections. Then $\\pi_*\\GL A_{\\zeta \\otimes B} $ is determined by a mostly degenerate spectral sequence and by a Wang differential \\[ d_k : \\pi_*(\\GL B) \\longrightarrow \\pi_{*+k-1} (\\GL B) .\\] We show that if $B$ is a $C^*$-algebra then the differential is given explic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4131","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"}